Hello everyone. Today we're going to be going over the January 2025 algebra 1 regions exam. In this video, we're going to be focusing on part one, which are the first 24 multiple choice questions. A link to this test can be found in the description of this video if you want to follow along at home. And this video is a part of a bigger series where I'm going to go over every single question from every single part of this exam. So videos going over part one, two, three, and four are found in the description of this one. And if you want help with algebra 1, algebra 2, physics, chemistry, and living environment regions, videos going over those tests are also found in the description of this one. That being said, let's start off with number one, which says when factored, the expression x cubus 36x is equivalent to what? So, whenever you want to factor an expression, what you want to do is you want to take out terms from it and repackage it or reformat it into parentheses, right? So if I have xubus 36x, I'm going to be looking at what term I can take out of both of these. So that term is going to be x because x cubed is just x * x * x and 36x is just 36 * x. So what do they have in common? Well, they have x in common. So if I take out x, I can by taking out x, I'm just writing it in front of the parenthesis and I'm writing what's left on the inside. So if I take out x, what's left? Well, x^2 is left and 36 is left. But this isn't any of our answer choices because for this we need to memorize that a^2 minus b ^2 is equal to a + b * a minus b. What we're left with is the difference of perfect squares. You need to remember x^2 is a perfect square. 36 is a perfect square. 36 is equal to 6^2 x= x^2. Right? So this is actually x^2 - 6^2 which we can rewrite as x + 6 * x - 6 which is going to be choice 3. Okay. This always appears in the regions. It's very important that you memorize that formula. Number two asks which equation represents the line that passes through the points -1a 8 and 4a -2. So in order to solve this problem, what we need to do is we need to find the equation of a line that passes through both of these points. The equation of that line is going to be y= mx + b. Okay, the m or the slope is equal to y2 - y1 over x2 - x1. And the b is going to be found by plugging in the points. So always we have to find the slope first and then we have to find the y intercept. Right? So we have these two points. We're trying to see what's the equation of the line that passes through both of them. So like I said the first thing we need to do is to find the slope. So we're going to have to assign one of these values to be x1 y1 x2 and x1 and and y2. So in this case we know that ordered pairs come in the format x comma y. So I'm going to say that negative 1 is x1 that 8 is y1 that 4 is x2 and that -2 is y2. So let's just plug this into this formula. Right? So here we have y2 which is -2 - 8 / x2 - x1 which is 4 -1. So this is equal to -10 over 5 which is equal to -2. So we know that our m or our slope is -2. Now that we've found our slope we plug it in. So now we have y is equal to -2x + b. And then in order to solve for b, we need to plug in one of the two points that we were given. So let's just plug in the first one. We know we already said that 8 is our y1. So we can just plug that into y. And we know that we already said that1 is our x1. So we can just plug that into x. So we're left with8 is equal to -2 * 1 + b. Or 8 is equal to 2 + b. Subtract two on both sides. We get that b is equal to 6. So if you plug in six, we get that y is equal to 2x + 6, which is choice one or -2x + 6, which is choice one. Number three asks, a geometric sequence is shown below. What is the common ratio? The common ratio is just a number that you need to multiply the last term by to get to the next term. Okay? And it's going to be the same for any geometric sequence. So really, they're asking you what number did you multiply all these terms by to get the next one. So if you don't know how to do it, all you have to do is take the last term, write it down, and then divide it by the previous term. So the last term was 32, the previous one was 8. So you can do 32 / 8 to get 4, or 32 over 8, and you get four. So the correct answer is 4. This makes sense because 1/2 * 4 is 2. 2 * 4 is 8 and 8 * 4 is 32. Number four asks what is the constant term of the polomial 2x cub - x + 5 + 4x^ 2. So the constant term is the term without an x. So which one of these terms has no x attached to it? That's going to be five. So the correct answer is one. Okay. Um anything else is going to change, right? The constant term doesn't change. Anything that has an x is always going to change because it depends on the value of x. If you plug in x equals 1 for this, you know this uh this will turn into two. This will turn into negative 1. This will turn into four. If you plug in x is equal to zero, this will turn into zero. Zero and zero. But no matter what you plug in, five will always be five, which is why it's the constant term. Number five says that a landscaping company charges a set fee for a spring cleanup plus an hourly labor rate. The total cost is modeled by the function C of X is equal to 55x plus 80. In this function, what does 55 represent? So in this case again we're using the formula y= mx plus b. So m or the number in front of the x is going to be your rate or your change or your ratio. And your b is going to be your initial fee initial fee or set fee or your constant. Okay. So this the m is your rate ratio or change. The b is your initial fee or your constant fee. Right? Um, so in this case we know that 55 is the thing in front of X. That's your M. That's going to be your rate change or ratio. Here we know that there is a set fee for spring cleaning. So the set fee has to be the B. So that's what 80 represents. 80 has to represent the set fee. Anything that does not have the X attached to it is is constant or set or non-changing. Anything in front of the X has to be the rate. So in this case, 55 has to be the hourly labor rate because that's what they described it to be. We know it's in front of x because it has a rate. 55 is a number in front of x. Number six asks us what this expression is equivalent to. So to solve this, all we need to do is distribute this negative sign or this negative one that's in front of this parenthesis and then just combine like terms. Right? You may be saying, well, where'd you get this negative one from? There's always an imaginary one in front of each one of these parentheses. So there's a one in front of this parenthesis and there's a one in front of this parenthesis as well. Right? The negative sign isn't just there. It's actually a negative one. So, let's let's um distribute this minus one. So, if we distribute this regular one, we're left with 5 x^2 - 2x + 4. But then we need to distribute this to break this part out of the parentheses because the only way we can combine combine these two together is if they're both out of the parenthesis. So, here I have -1 * 3x^2 which is -3x^2 -1 * 3x which is -3x and 1 *1 which is positive 1. From here I can just combine like terms. 5x^2 - 3x^2 is 2x^2. -2x - -3x is - 5x. And finally pos4 + 1 is pos5 which is going to be choice two. Number seven says a system of inequalities is graphed on the set of axes below. What is the solution to the system? So the solution to the system is pretty much the solution to both of the lines. the system is one or more lines. Okay, so in this case, the shaded region is going to be the solution to each line. So the solution to this line is this red shaded region. Okay, the solution to this dashed line is going to be this green shaded region. It's wherever the lines go. Okay, wherever they're shaded in. So the solution to the system is the solution to one or more of the lines. So in this case, we have two lines. So the solution to the system is the solution of both of the lines, right? Or this overlapping pattern here that I'm drawing an S over. So any point inside of this region is going to be the solution. Okay? Any point that's on a dashed line is not a part of the solution. So if we look at these points, it can't be one comma 1 and it can't be 2, 2. That's because 1 comma 1 lies on this dashed line. It lies right on one of the dashes, right? This is not a part of the solution. The dashes indicate that whatever's on this line is not a part of the solution. Sure, whatever is to the right of it is a part of the solution, but whatever is on it is not. Okay? The same thing goes for 2, -2. 2, -2 is uh right here, right? Again, that's on the dashed line, which means that it's not a part of the solution. Right? That leaves us with choice four is the correct answer. Four comma 2 is one, two, three, four. One, two. That's right here. That's right in between those intersecting lines which means it has to be our solution. It can't be choice three because again 1 comma 8 is all the way up here. This is a part of the solution of the dashed line but it's not a part of the solution of the solid line. The solution of the system is the solution of both of the lines. So that's why it has to include both. Number eight says in an arithmetic sequence the first term is 25 and the third is 15. What is the 10th term of the sequence? So an arithmetic sequence is just a bunch of numbers that are related by a rule. So in this case 1 2 3 4 and five is an arithmetic sequence because you have to add one to get to the next term. Okay, the amount that you're adding by is called your common difference. Okay, so just like in a geometric sequence we have the common ratio, here we have the common difference. Okay, so we know that the first term is 25. We don't know the second term, but we know that the third term is 15. Okay, we know that we're going to be increasing or decreasing by the same amount per this entire sequence. Okay, so in this case, we started with 25, we ended with 15. That means that we had to decrease, but we had to decrease once in order to get to two or the second term, and then we needed to decrease a second time to get to 15. We don't know what we're decreasing by. So, we know that when we decreased two times, we went from 25 to 15, which means that we went down by 10. That means that every single hop here or every single change has to be min -5 and minus5. That makes sense because 25 - 5 is 20 and then 20 - 5 is 15. So if we want to find the 10th term, let's just continue subtracting five until we get to the 10th term. So this is the third term. The fourth term is just 15 - 5 which is 10. Then the fifth is five. The sixth is 0. The se uh the seventh is neg 5. The eighth is -10. The ninth is -15 and the t and the 10th is -20. Okay, so literally just keep it running. Every single one of these just keep subtracting five from it until you get to the 10th term at which you're going to get -20. Number nine asks you to rewrite this formula for p for w. Okay, so right now this formula is is written in terms of p. We know that p is equal to 2 l + 2 w. But we want this equation to be written or solved for W. So when we solve for a variable, we just rewrite it with that variable alone. Okay? So in order to get 2 W alone, I need to subtract 2 L from both sides. So I get P - 2 L is equal to 2 W. Now we're solving for W, not 2 W. So we'll divide both sides by two, and we get that P - 2 L / 2 is equal to W, which is choice two. Number 10 says, "Market Street Pizza kept a record of pizza sales for the month of February. The results are shown in the table below. Of all the pizzas sold in February, what percent were plain deep dish pizzas?" So percent is just part over whole. Okay, the first part of this question tells you the whole. Anything after the comma tells you the part. So the second part of this tells you the part. Okay, so of all the pizzas tells you the whole. of all is the same thing as saying out of or looking at. Okay, so looking at all of the pizzas sold in February, which is everything in this chart, that's our whole. What percent were plain deep dish pizzas? So we're looking for plain pizzas, which is in this column, that were also deep dish. So that's 200. So I know my part is 200, and my whole is everything inside of here. So to find my whole, all I have to do is add everything inside of here. That's going to equal to 1,00. So, there's 1,000 pizzas sold. And of those 1,000 pizzas, well, 200 of them were deep dish and plain. So, 200 over 1,000 is equal to 20%. So, number 11 asks, when solving -2 * 3x - 5 is equal to 9 over 2x - 2, what is the solution? So, all we have to do is just solve for x. So, what I'm going to do is I'm going to have to break these out of these uh this 3x - 5 out of the parentheses by multiplying it by -2. So, -2 * 3x is -6x. -2 * 5 is pos 10. And this is equal to 9 / 2x - 2. So, I'm going to get x on its own and I'm going to move x to this side. So, I'm going to add 2x or I'm just going to add two on both sides and be left with -6 + 12 is equal to 9 / 2x. Then I'm going to add 6x to both sides and I have 12 is equal to 9x / 2 + 6x over 1. Okay. Um, remember that 9 over 2x is the same thing as saying 9x over 2 or 9 * x over 2. The reason why I wrote 6x over 1 is because I'm going to have to add both of these uh fractions together. In order to add fractions, I need I need them to have the same denominator, right? So in this case, the denominator of any whole number is just one. So 6x is the same thing as saying 6x over 1. What's the lowest common denominator between 2 and 1? Well, it's going to be two. So how do I convert this denominator of 1 into a denominator of 2? Well, I multiply by 2 over2. So I know that 12 is equal to 9x / 2 + 12x / 2. That's equal to 21x over2. Don't add the denominators. So I know that 12 over 1 is equal to 21x over2. Whenever you're trying to solve for the value of x and it's in a fraction and it's equal to a whole number, always cross multiply. It's the easiest way to solve it. So by cross multiplication, you multiply the numerator by the denominator. So 12 * 2 is 24 and 24 is equal to 1 * 21 x, which is 21x. So I'm going to divide both sides by 21 and I'm going to get 24 out of 21 is equal to x. Don't panic if it's not your answer choice or if it's not in the answer choice. Just simplify it. So 24 over 21. If I divide the top and the bottom by 3, I get that uh 24id 3 is 8 and 21 / 3 is 7. So 8 over 7 is equal to x, which is choice one. Number 12 says that the expression 2 x ^ of 2 a + b is equivalent to what? So for this you need to remember the specific rule x ^ of a * x ^ of b is equal to x ^ of a + b. So if you have two exponents that are um that have the same base and you multiply them, you're pretty much going to add their exponents together. So for example, 2^2 * 2 cubed is equal to 2 ^ of 2 + 3 or 2 ^ 5. Okay, this makes sense because 2 is 2 * 2. 2 cubed is 2 * 2 * 2. In this case, you have 2 * 2 * 2 * 2 * 2 or 2 multiplied by itself five times. Okay? So that's how we do this here. So if we ever want to split this up, it's not going to be addition. It's going to be multiplication. It's going to be x to the power of something * x to the power of something else. In this case, choice 3 has to be the correct answer because x ^ of a * x ^ of a + b is equal to x ^ of a + a + b. So a + a + b. Well, a plus a is equal to 2 a. and 2 a + b is equal to 2 a + b. That's our exponent over here. Choice four is wrong because that would get us x ^ of 2 a + 2 b. Okay, number 13 says the inputs and outputs of a function are shown in the table below. The first thing that I want to notice here if I'm trying to describe the function is the change is my change constant and the answer to that is no because in order for us to go from 1 to two, our y changes by 0.125. Then for us to change from 0.25 25 to 0.5 we change by 0.25. Then to change from 0.5 to 1 we change by 0.5 and then we change by one. So our rate of change is not not constant. So that means that it can't be a linear equation or an absolute value equation. For something to be a linear equation, the rate of change is constant. And an absolute value is literally just two linear equations stuck together. So an absolute value also has a constant rate of change. Okay, that means that this has to be an exponential growth. The reason why it's not quadratic is because there's no negative values, right? A quadratic formula would look something like this. It would look like u for x^2 it would look like um when x is 1 0 1 it would look like or let me just get better values I guess. Let's say that when x is equal to -2 negative 1 0 1 and two the y would equal to um pos4 1 0 four uh 1 and 4 right so you would have this symmetry um in the negative side and the positive side we don't have any negative numbers here so this must be an exponential function okay the other way you could have done this was you could have plugged this into your calculator gone into stats edit place this data inside of that list. Okay. Then went into stats again, calc, and you would have run a linear regression, a quadratic regression, and an exponential regression. And whichever one of these tests gave you an RV value that was closer to one would have been the correct answer choice. In this case, an exponential function gives you an RV value of one. So that's how you know that this is the strongest fit. Okay? Everything else would have given you a smaller RV value. Number 14 says that Stephanie is solving the equation x^2 - 12 is equal to 7 x - 8. Her first step is shown below. Which property justifies her step? This is going to be the addition property of equality. Okay. What she did here was was she got rid of this eight. So this was the original equation and this was her first step. Notice how it's missing the minus 8. In order for us to get rid of the minus 8, we have to add eight to both sides. Okay. So if we're adding eight to both sides, that the that's the addition property of equality. Choices one and three are wrong because these have to deal with multiplication. And choice two is wrong because the commutative property is on the same side of the equal sign. Right? This happens on both side of the equal both sides of the equal sign. The commutative property occurs only on one side of the equal sign. Okay. Number 15. The sum of 8 rad 3 and rad 3 is the same thing as saying like 8x plus x. So that's the same thing as 9 radical 3. Okay. The way I like to approach this is well I don't know the value of radical 3. If I plug it into my calculator, if I plug radical 3 into my calculator, I get this messy number, right? This goes on forever. So if I don't know the exact value, I can just replace it with x. So 8x plus x is just same same thing as saying 9x. Okay? If you want to know a real reason, 8 radical 3 is the same thing as saying 8 times radical 3 or radical 3 added to itself eight times. Right? So 1 2 3 4 5 6 7 and 8. Okay. If I add another radical 3, I'm now adding it to itself nine times. Number 16 says the dot plot below represents the test scores for 20 students on a math test. The mode for the test is 80 and the median is 85. Which dot plot correctly represents this data? So the mode is the most repeated data point. So if I have the data set like one one one two three four, my mode is going to be one because it's the one that appears the most in the data set. Okay, the way that you um read a dot plot is each one of these dots is a data point. Okay, so if you have one data point on 65, that means that 65 appears in your data once. If you have two dots above 70, that means that 70 appears in your data twice. Okay, so we know that our mode has to be 80 cuz they say so here. That means that if each one of these is a data point, 80 should be the tallest tower, which is why choices four and two are wrong, right? Because choice two says that 85 has the most amount of data points, right? Each dot is a piece of data pertaining to that number. So in this case, you have 1 2 3 4 5 six. You have six dots above 85, meaning that 85 is repeated six times because nothing else is taller. That means that 85 is the most repeated. That's false because we want our mode or most repeated value to be 80. So the tower of dots should be the tallest around 80, which is true for choice one and three. Right? This says that it's repeated 1 2 3 4 5 six times, which is the most out of any other piece of data. So now we need to find the median. The way you find a median on a box plot is you look at what value is in the middle. So if you have a regular set of data like 1 2 3 4 and five and you you want to find the median here all you do is you find the middle value by crossing out one from the left one from the right one from the left and one from from the right. Whichever value is left in the middle is your median. Okay. The thing with a box plot is that it automatically sorts your data from least to greatest which is what you need the data to to be in in order to find that middle value. So all you have to do here is literally just cross one dot on the left side and one dot on the right side until you're left with one in the middle. So for choice one, if we cross out one on the left, one on the right, like so. We're actually left with this data point which lies on 85. So the data point that's left is the middle data. As we can see here, three was the middle data. As we can see here, the number remaining is representing 85, which means that our median has to be 85. And choice one is the correct answer. Okay. The reason why it's not three is because the median for three was 80, which is our mode, not our median. Number 17 says, a function is graphed on the set of axes below and it's asking us for the domain of the function. So the domain of the function is all x values that the function exists on. So in this case the function starts when first of all when you read a function from the left side to the right start from the uh to the right side. Whenever a function has a open dot or a closed dot that means two different things. Both of these can represent start or end points. Okay? If they're on the left side, they represent a start point. So, we know that the graph starts at -2. Okay? So, all of the x values start at -2 and then go on until infinity. How do I know they go on until infinity? Because this arrow, whenever you see an arrow on a graph, that means it goes on forever or until infinity. So, that's the first thing, right? So, we know the domain has to start at two. So it has to be any value that's greater than two. Which is why two choices three and four are wrong because they're saying that x is greater than four or neg4. The graph literally starts only at -2. Okay. The second thing you need to know here is that whenever you have an open circle that's either a greater than or a less than symbol. Whenever you have a closed in circle that's a greater than or equal to or a less than or equal to symbol. So that's why it has to be choice one because it has it accounts for that open circle which has to be a greater than symbol. And this makes sense, right? A open circle means it's not included. So -2 is actually not included in the domain. All of the values after -2 are included. How do we know that? Because we're using a greater than sign. So if if x is greater than -2, x cannot be -2. Okay? It has to be something bigger. Um, so we started on we know that the dots represent start or end points. If they're on the left, they represent start points. We have to start at -2. It's an open circle which means that x has to be greater than -2. If you're confused about this line here, this line literally just means is. So if we translate this into English, x line is so x is greater than -2. Okay, number 18 asks which ordered pair is a solution to the equation y - 1 is equal to 2 * x + 1/4. The way that you do this, an ordered pair is a solution if it number one if it exists on the line or if it makes the equation true. So any pair or any one of these ordered pairs that is actually on this line will make this equation true. Okay? So all you have to do here is just plug in these points and see which one actually gives you a reasonable answer. So before we do that, I'm just going to go ahead and combine this and simplify this equation to make it easier for myself. Okay, so if we look at here or if we look at this right here, um we can expand this two out. So we can multiply 2 and x to get 2x and 2 and 1/4 to get 2 over 4 or um 0.5. Okay, so we have y - 1 is equal to 2x + 0.5. If I add one on both sides, I get y is equal to 2x + 1.5. The reason I convert it into a decimal is because all of my values that I'm going to plug in are decimals. And it's easier to deal with a decimal than adding a decimal to a another decimal than it is adding a decimal to a fraction. So now to see which ordered pair lies on this on this line or this equation, I need to plug these into the equation. So remember the first pair or the first number is going to be your x. The second is going to be your y. So let's plug in the first point. We have y is equal to 0.75 * 2 plus 1.5. And we know that our y is equal to 0. So let's do this. 0.75 * 2 is 1.5. 1.5 + 1.5 is 3. Is 0 equal to 3? No. 0 is equal to zero. So it can't be choice one. Let's try choice two. It says that four, which is y, has to equal to 1.25 * 2 + 1.5. Okay. So four has to equal to 2.5 + 1.5. 2.5 + 1.5 is four. So four is equal to four. Is this true? Yes, four is equal to four. So choice two is the only answer choice that makes this equation actually true. If you plug in three and four, you'll get like 7 is equal to 2, which is false, or that 5 is equal to 6, which is also false. Number 19 says, uh, Elena's fastest time for a 50 meter dash is 7 seconds. She wants to know how fast this is in inches per meter, uh, inches per minute. Which expression can she use for the correct conversions? So right now she has her speed in terms of meters per second. How do I know? Well, that's because she measured her distance which is in meters over seconds. So now she So first of all her speed right now is in meters per second. Okay. Whenever you have meters or any unit followed by per another unit, you know that this is going to be your numerator. This is going to be your denominator. And the purr just counts for the line. So anything before the purr goes on top like we had over here. Anything below after the purr goes on the on the bottom. So now she wants to convert this into inches per minute. So following that rule, inches goes on top. Purr counts as that line and minutes goes on the bottom. Okay. So the way that we convert meters to seconds to inches per minutes is by multiplying it by, you know, opposite conversions. Okay. So first of all, we can eliminate choices one and two because they start at seconds over meters, which is wrong. We want meters/ second or meters over seconds. Okay, so that's why these are wrong. Remember that speed is always a distance over time, not time over distance. Now, in order to see if three or four are right, we need to see what units cancel out. So if we look at choice three, if we were to multiply all of this out together, right? the seconds would cancel out because anything on the denominator and numerator if they're the same number or the same unit they'll cancel out. So here these two guys will cancel out but that's it. So if I were to multiply the rest of this I will get 50 m squared / 39.37 minutes time in remember we want our answer to be inches over minutes. Sorry, we want uh yeah, inches over minutes. Is meters squared over minutes time inches the same thing as inches over minutes? No, that's a different unit. We don't want that unit. We only want inches per minutes. If we look at choice four, we can see here how the seconds and the seconds will cancel out. The meters and the meters will cancel out. And what we're left with is seven minutes over 50 time 39.37 in. Forget about the numbers because the numbers don't even matter here. What matters is that we're left with inches on the top, which is what we wanted, and minutes on the bottom, which is also what we wanted. So, choice four is the right answer. Focus only on the units that cancel each other out. That's all you have to do here. No math involved. For number 20, it says the table below shows the highest temperature recorded in August for several years in one town. And it's asking you for the interquartile range. So, the interquartile range or the IQR is equal to uh quartile 3 minus quartile 1. The way that you find this out is by using your calculator. There's no other way or there's no other faster way. So, you go into stats, you go into edit, and you're pretty much going to plug in all of this data in in temperature into this um table. You're not going to plug in the year because the year doesn't matter here. We only care about the temperature. So, you're going to go ahead and put 86 and fill the rest out. So once you have the data filled out, you're going to go and press stat again. You're going to go into calc and then you're going to press enter. Um once you highlight one one variable stat or one var stats if you press enter press enter two more times and it'll calculate all of the statistics or the stats for you. So here you're looking for the IQR which is Q3 minus Q1. If you can see here Q3 stands for the third quartile which is 90.5 and Q1 stands for the first quartile which is 79.5. So you do 90.5 - 79.5 as your IQR and that is equal to you plug it into your calculator that's equal to 11. So that's choice three. Number 21 asks the function of f ofx is equal to x^2 is multiplied by k. We know if k is less than -1 which graph could represent g ofx is equal to k * f ofx. So what what matters here is that you have you have x^2 and you're multiplying it by k. What you know about K is it's a number that's less than negative 1, which means that K is negative. So the rule here is that X squ normally looks like this. If you multiply X^2 by a negative number, for example, like -2, it then flips its direction. So if you're confused about this, go ahead and plug it into your graphing calculator. Go Y equals, press X^2, and then graph any value um that's less than1. So let's say -3 * X^2. So like I said, x^2 is going to be facing up. And then any number that's less than -1 * x^2 is going to be facing down. So choices 1 and three are out because g of x, which is that number time x^2 is facing downwards. And the correct answer has to be four because our resulting graph is a little bit slimmer than our original graph. Right? Remember that if you add a number in front of x squar or a quadratic, that determines how skinny or how wide it is. right? It determines its narrowness. If you're multiplying by a number like 1/4 orgative - 1/4 orgative - 1/2, that's going to make the equation wider. But if you're multiplying by a number like -2 or -4 or anything that's not a fraction, it's going to make it more narrow. Number 22 asks, which graph is the solution to the inequality 6.4 - 4x is greater than or equal to -2.8. So all you have to do here is just solve for x. So you're going to do that by adding 2.8 8 to both sides. So you're going to get 9.2 - 4x is greater than or equal to 0. You're going to move the 4x onto this side and you're going to get that 9 9.2 is greater than equal to 4x. If you divide both sides by 4, you're going to get that 2.3 is greater than or equal to x. So now what you know, you should remember this from uh the inequality problem. You should know that a empty circle represents greater than or equal to and a shaded in circle represents greater than or uh sorry a empty circle represents greater than and less than. A shaded in circle represents greater than or equal to or less than or equal to. Okay, so in this case we're dealing with a a greater than or equal to sign. So we're not going to choose choice one or two because they have the empty circles. Then what you also need to know is that wherever the arrow is, that's where your answers are also going to be. Okay? So in this case, which one of these has the right answers? That's going to be choice four. The arrow is facing in the direction of the numbers that are smaller than 2.3. Remember, x has to be smaller than 2.3. 2.3 is bigger than x. So it has to be facing in the direction where the numbers are smaller. Two or choice 2 is facing in the direction where the numbers are bigger. 23 says the number of fish in a pond is eight more than the number of frogs. The total numbers of fish and frogs is at least 20. If x represents the number of frogs, which inequality can be used to represent the situation. So we know that the fish is equal to eight more. More means add. 8 means 8. So it's eight more than number of frogs. We know that x represents the number of frogs. So fish is equal to x + 8. We know the total amount of animals in the pond is the number of fish plus the number of frogs, which is x. So if we want to represent this all in terms of frogs, we can plug in 8 plus x into the fishes. We already know that fish is equal to 8 plus x. So why don't instead of writing fish, let's just write 8 plus x. So the total number of frogs and fish is just fish plus x or 8 plus x plus the number of frogs, which is x, which is equal to 8 + 2x. And we know that the total number of fish and frogs is at least 20. So the smallest number that 8 + 2x can be is 20. So it has to be greater than or equal to 20. Remember that at least always means greater than or equal to. And this is going to line up with choice four. Number 24 says the graph below represents a function that is always decreasing over the entire interval. -3 is less than x which is less than 3. So we're looking only at this interval. So my advice to you all is to restrict your graphs to this interval. Otherwise you'll get confused. So you can cross out everything that's outside of this interval from -3 to positive3. So if you cross everything else out, what you're going to be looking for is you're going to see which which graph is going to be always increasing or always sorry, always decreasing. So the graph that's always decreasing is the line that's going towards the bottom right corner of your page. So that's this corner of your test booklet or your page. Okay? So after we've we've um kind of separated our interval from our non-interval, which one of these lines is going to the bottom left? Well, it can't be choice one. Choice one is increasing, right? You read the graph from left to right. So in this case, this graph is starting from here and it's going to the top right of the page. That means that it's increasing. The same thing happens with choice three. You read the graph from the left to the right. You can see that it's starting from up here, but it's then increasing slowly towards the top right of the page, which means that it's increasing, right? We want it to go to the bottom right corner. Choice two is interesting because we can see that it's increasing, but then it begins to decrease. But our problem wants us to be always decreasing. So, it can't be choice two because we're increasing partially. Choice four is the right answer because we're always decreasing. If we read it from the left to the right, we started up here and we went down here. We're going to this bottom right corner. Okay, so that is the last question in this multiple choice section for part one. If you want to go over part two, again, the link to that video is in this description. If you want more regions help on the living environment, physics, chemistry, um, US history regions, a link to those playlists and those videos can also be found in the description of this one. If you have any questions about any of the topics or questions that I went over in this video, please let me know in the comments below. I'll try my best to answer them. And I hope you guys learned something.