in this video we're going to focus on solving twostep equations so let's start with the basics we're going to cover equations with fractions parentheses variables in both sides and even decimals but let's start with the basic two-step equations so how would you solve this equation let's say that 3x + 5 is equal to 17 what's the first thing that we need to do in this problem in order to solve this equation we need to isolate the X variable so the first thing we need to move is the five we want to get X by itself on the left side so we need to get rid of the five since the five is added to 3x let's perform the opposite operation let's subtract both sides by five five and neg five those two will cancel so what we have left over on the left side of the equal sign is 3x 17 - 5 is 12 now all we need to do is separate the three from the X the opposite of multiplication is division so we need to divide both sides by three so X is 12 ID 3 which is 4 and this is the answer here's another example that you could try 4x + 3 is equal to 19 So based on the last example take a moment and work on this problem feel free to pause the video now just like before we're going to start with subtraction let's subtract both sides by three just to get rid of the three on the left side 3 and neg3 they add up to zero so we just have 4X on the left side and on the right side it's going to be 19 minus 3 which is 16 next to separate the four from the X we need to divide both sides by four 4 ID 4 is 1 1 x and x you can just write as X on the right side it's 16 / 4 which is four and so that's the answer for this problem X is equal to 4 let's try a similar example but slightly different so let's say that 17 - 5x is equal to 2 if that's the case what is the value of x so what do you think we need to do in this problem well we need to get rid of the 17 first on the left we have positive 17 so we need to begin by subtracting both sides by 17 so these two will add to zero and then we could bring down the 5x pos2 - 17 that's equal to -5 next let's divide both sides by5 5 ID by itself is 1 leaving behind 1 X-15 /5 is pos3 whenever you divide by two negative numbers you're going to get a positive result and so that is the answer X is equal to 3 now let's move on to our next example consider this equation 9 is equal to 3 + x / 4 so we have a fraction what do you think we need to do in this problem well in this problem we could start by subtracting both sides by three just as we've been doing 9 - 3 is 6 now let's bring down the fraction so 6 is equal to x / 4 the opposite of division is multiplication so since X is divid 4 to get rid of that let's multiply both sides by four on the right side the fours will cancel leaving behind an X variable on the left we have 4 * 6 which is 24 and so that is the answer now if you want to check your work you can take this answer and plug it into the original equation so 9 is equal to 3 plus let's replace x with 24 24 / 4 is 6 and 3 + 6 is 9 so 9 equal 9 the equation is balanced which means that this here is indeed the right answer X is indeed 24 now let's move on to our next problem go ahead and take a minute and try this example so 8 + x / 3 is equal to 12 so pause the video and write this equation down go ahead and solve it so I'm going to start off by subtracting both sides by eight 12 - 8 is 4 now in The Next Step I'm going to multiply both sides by three so on the left the threes will cancel on the right we have 4 * 3 which is 12 and so that's going to be the answer for this problem X is equal to 12 here's another one that you could try so in this example the X variable is is on the right side so go ahead and try so this problem is very similar to the first two problems that we covered even though the X variable is on the other side the same rules apply let's begin by subtracting both sides by two so 14 - 2 that's 12 and on the right side these will cancel just as before and as you can see solving these equations they're not that difficult now we need to divide both sides by three and so X is going to going to be 12 ID 3 so X is 4 in this example now sometimes you may have multiple X variables like in this problem 3x + 8 + 5x let's say this is all equal to 32 now what should we do in this example now this problem might require more than two steps so it might be a multi-step problem which I'll have more later in this video but what do you think we needs to do in this problem if you see two x variables on the same side the first thing you should do is combine like terms so we should add 3x and 5x which is 8x now we have a problem that's similar to the ones that we dealt with in the beginning so let's go ahead and subtract both sides by8 8 - 8 is z we can bring down the 8X and on the left side we have 32 - 8 which is 24 and now let's divide both sides by 8 so 8X / 8 is simply x 24 divid 8 is three and therefore this is the answer X is equal to 3 now it's your turn go ahead and work on this problem let's say that 7 x + 2 - 3x is equal to 26 so pause the video and try that so let's let's begin by combining like terms let's combine 7 x and -3x 7 - 3 is pos4 so we have POS 4x + 2 which is equal to 26 next let's subtract both sides by two 26 - 2 that's going to be 24 and let's bring down the 4X now we need to separate four from X so let's divide both sides by four 4X ID 4 is X and 24 ID 4 is 6 and so that's the answer X is equal to 6 now sometimes you may have a variable found on both sides of the equation so what do you think we need to do in this problem in this problem what you want to do is you want to move all the X variables to one side of the equation and all the numbers to the other side so let's move the 5x from the left to the right side so we can accomplish that by subtracting both sides by five now simultaneously we can add eight to both sides we can move all the constant terms all the numbers without x to the left side the eights will cancel and the 5x will cancel so on the left we just have a number 4 + 8 is 12 on the right side we have a variable 8x - 5x is 3x so now all we need to do is divide by three at this point and so X is equal to four and that's it so that's how you can solve that equation here's a similar example 13 - 2x is equal to 4X so now it's your turn go ahead and work on that problem so now what I'm going to do is add 2x to both sides and at the same time I'm going to add five to both sides doing it this way will allow me to get rid of all the X variables on the left and all the constant terms on the right so on the left I just have 13 + 5 which is 18 and on the right 4x + 2x which is 6X so now all I need to do is divide both sides by six and so X is going to be 18 / 6 which is three sometimes you may have parentheses in the equation like this one let's say that 3 * 2x - 4 + 1 is equal to 7 so what do you think we need to do in order to solve this particular equation what ideas do you have what we need to use is the distributive property we need to distribute 3 to 2x - 4 so first let's multiply 3 * 2X that's going to be 6X next let's multiply 3 by -4 and add to -2 and let's rewrite everything else now our next step is to combine like terms -12 and 1 are like terms on the same side so -2 + 1 we can exchange that for1 since they're equivalent to each other now all we need to do at this point is First add 11 to both sides and then we could divide right now we have 6X which is equal to 7 + 11 which is 18 and then we could divide by 6 18 ID 6 is 3 and so that's our answer X is equal to 3 here's another problem that's let's try a similar problem first go ahead and try this one so let's begin with the distributive property let's multiply 5 by 3x just like we did before and so that's going to be 15x next we have 5 * 4 which we know it to be 20 and then let's rewrite the other stuff now let's combine like terms we can add 20 and two which we know it's going to be 22 so we have 15x + 22 which is equal to 37 now our next step is to subtract both sides by 2 2 37 - 22 that's 15 so now all we need to do is divide both sides by 15 15 divid by 15 is 1 and so that's going to be our answer X is equal to 1 now sometimes you may have parentheses on both sides of the equation so let's try an example that illustrates that so let's say we have 2 + 4 * 3x + 2 and let's say that's equal to 3 - 4 times well let's change that let's say it's 2 * 5x + 1 + 14 so using what you know go ahead and solve this particular equation find the value of x so we need to use distributive property first let's multiply 4 by 3x and then by two 4 * 3x is 12x and 4 * pos2 that's equal to 8 on the right side we need to multiply 2 by 5x which is 10 x and then 2 * 1 which is 2 now let's combine like turn terms on the left side we can combine two and 8 on the right side 2 and 14 now 2 + 8 adds up to 10 and 2 + 14 is 16 so now let's isolate the X variables let's subtract both sides by 10 x so doing this will give us an X variable only on the left side and let's subtract both sides by 10 so that we're going to have a constant number on the right side 12 12x - 10 x is 2x 16 - 10 is 6 now all we need to do is divide by two 6 / 2 is three and so X is equal to three and that's the answer here's a similar problem that you could try let's say that five - 2 * 3x + 4 is equal to 3 - 4 * 2x + 1 So based on the last problem go ahead and try these problems so let's start with the distributive property let's multiply -2 by 3x that's going to be -6x and then let's multiply -2 by 4 which is8 on the right side let's start start with -4 * 2x that's -8x and then4 * 1 which is4 now let's combine like terms so we can combine those two on the left and 3 and4 on the right 5 - 8 that's going to be -3 and 3 - 4 is-1 now let's add 8X to both sides this will give us an X variable on the left side and it's going to be positive and let's add three to both sides so we can get a constant term on the right side -6x + 8x is 2x -1 + 3 is 2 so if we divide both sides by two we see that X is going to be 1 and that's it for that problem now sometimes you may have multiple fractions we covered an example where we only had one fraction in the equation but here's an example with two fractions now there's different ways in which you could solve it you could try to add one to both sides first to simplify the equation or you could just from the beginning eliminate all fractions which sometimes I like to do notice that we have a denominator of three and two what is a common multiple of two and three a common multiple of two and three is six so if we multiply everything by six we can get rid of all fractions so let's multiply 6 by 2x / 3 6 * 2x is 12x 12x / 3 well that's going to be 4X so 2/3 of 6 is 4 next let's multiply 6 by 4 6 * 4 is 24 and then let's multiply 6 by 3x / 2 6 * 3x is 18x / 2 that's a 9x and then 6 * 1 is -6 and now this looks similar to equations that we've solved before so let's begin by subtracting both sides by 4X and simultaneously let's add six to both sides 24 + 6 is 30 9 x - 4x is 5X now all we need to do is divide both sides by 5 30 / 5 is 6 so X is equal to six and that's the answer for that problem here's a similar problem but this time there going to be three fractions in the equation so go ahead and try this problem now let's find the least common multiple of four and five a quick way to find just a common multiple four and five is to multiply the two numbers 4 * 5 is 20 so if we multiply every fraction by 20 we can completely eliminate the entire equation of all fractions so let's do that let's multiply 20 by 3x / 4 now 20 * 3x is 60x 60x / 4 is 15x instead of multiplying first and then dividing you could divide first and then multiply if we did 20 ID 4 that's 5 5 * 3x will give us the same answer of 15x now what about 2 fths of 20 well if we take 20 divid by five that will give us four and then four * 2 is 8 so two fths of 20 is 8 now if we multiply 83 over 20 by 20 the 20s will cancel giving us 83 and now let's solve let's subtract both sides by eight 83 minus 8 is 75 and now all we need to do is divide both sides by 15 75 divided by 15 is five and so that's the answer now sometimes you may have to deal with decimals let's say we have 2X +. 3 which is equal to 1.5 now you can go ahead and solve it or you can eliminate all decimals now every decimal in this equation is round into the the 10's place so to get rid of all decimals all we need to do is multiply everything by 10 2x * 10 is 2x 3 * 10 is 3 1.5 * 10 is 15 and now we could solve it like any other problem so let's subtract both sides by three 15 - 3 is 12 and then we divide by two we can see that X is equal to 6 here's the last example in this video so as you can see all the numbers are rounded to the hundreds place so what do you think we need to do in this problem let's multiply everything by 100 so basically you just need to move the decimal two units to the right 100 * 28x is 28x 14 * 100 is 14 13x * 100 is 13x and 74 * 100 is 74 and now we just got to solve let's subtract both sides by 13x and also by 14 so 28 - 13 is 15 74 - 14 is 60 60 / 15 that's equal to four and that's the answer for this problem now I want to show you one of my algebra courses that might be useful to you if you ever need it so go to udemy.com now in the search box just type in algebra and it should come up so it's the one with the image with a black background so if you select that option and if you decide to go to course content you can see what's in this particular course so the first section basic arithmetic for those of you who want to focus on addition subtraction multiplication and division and it has a video quiz at the end it's a multiple choice video quiz you can pause it work on the problems and see the solutions it covers long division multiplying two large numbers and things like that the next tutorial is on fractions adding subtracting fractions multiplying dividing fractions converting fractions into decimals and so forth so you can also take a look at that next solve the linear equations which we covered and just more examples if you need more help with that the next topic order of operations which is also useful uh graph in linear equations you need to know how to calculate the slope needs to be familiar with the slope intercept form standard form and just how to tell if lines are parallel perpendicular and so forth and there a quiz that goes with that as well the next topic is on inequalities and absolute value Expressions which are also see in a typical algebra course and then we have pols and that's a a long section and then factoring you just that's another topic you need to master and then system of equations you can solve it by elimination substitution there's also word problems as well sometimes you got to solve equations with three variables X Y and Z so that could be helpful next quadratic equations how to use a quadratic formula how to graph them how to convert between standard and vertex form and then you have rational expressions and radical expressions solving radical equations simplifying it things like that and every section has a quiz so you can always review what you've learned if you have a test the next day so here we have complex imagine numbers you need to know how to simplify those exponential functions logs I have a lot of videos on logs and then this is just functions in general vertical line tests horizontal line tests how to tell functions even or odd and then conic sections graph in circles hyperbolas ellipse is parabis and things like that there's two video quizzes because it's actually a long section and finally arithmetic and geometric sequences and Series so that's my algebra course if you want to take a look at it and uh let me know what you think