[Music] welcome to moomoomath today we are looking at the 7th grade math year and review part 2 so we're gonna start by solving some equations so we've got x over 2 is equal to negative 14 when we're dividing a variable what we need to do is do the opposite operation so we're going to multiply by 2 on both sides and to keep our equation equal we multiply okay when we multiply by 2 the 2's cancel and we're left with X so X is equal to and then we just multiply the right side which is negative 28 and that's how we handle division okay so now let's look at a two-step equation we have 3x minus 6 is equal to 15 to solve for X we're gonna add 6 to both sides and that gives us 3x because the 6 is cancelled is equal to 15 plus 6 is 21 and then since it's 3 times X is equal to 21 we want to divide to do the opposite operation so we get x equals 7 so there's how we solve a two-step equation now this is another two-step equation but this time our variable is negative okay we want to isolate the X so we're going to move the 2 to the other side now be careful because the 2 is actually positive so in order to move it we have to subtract it so bringing this down 2 minus 2 is 0 we have a negative 4 that we bring down and then 26 minus 2 is 24 and then we want to divide both sides by negative 4 because you want the X to be positive and negative divided by a negative is a positive and then you have 24 divided by negative 4 is negative 6 so there's the first part with our two step equations now let's move to a little more complicated problem this is where we have more than one variable on that side so what you want to do is look at the equal sign and simplify the left side so we have like terms 5x and 2x we want to actually combine these two like terms so 5x plus 2x is 7x now we're going to bring down the constant and it's negative 7 is equal to 42 now we have a two-step equation just like we worked so we're going to add 7 to both sides and that's going to give us 49 so 7x is equal to 49 divided by 7 so X is positive 7 so that one was a little bit more involved because we had to simplify before we moved anything around now the next problem we are going to have to use what's called the distributive property when you have five times a quantity we have to multiply everything in that parenthesis by the 5 so 5 times X is 5x and 5 times negative 3 is negative 15 that's equal to positive 15 now we have a two-step equation so let's add 15 to both sides and that leaves us with 30 on the right side the 15th cancel and I bring down my 5x now 5 times what gives us 30 we're gonna divide by 5 so X is 6 so that's how we solve one with a distributive property so now this next one we have a distributive property and we have to simplify so we're kind of getting more complicated each time so the first thing we want to do is distribute that negative 2 so distribute it into the parenthesis so that gives me negative 6y negative 2 times negative 6 is positive 12 bring down the negative 7 and then the neg equal to 16 now we can simplify the left side we have two constants so negative 6 plus five is equal to 16 the five came from combining the negative 12 minus 7 now we have a two-step equation so move your content first so we get negative 6 the 5s cancel equals 16 minus 5 is 11 and then we divide by negative 6 and we end up with y equals 11 over negative 6 or negative 6 11 so I tend to put the negative on the top okay so that's distributing and combining now let's look at some inequalities ok so here are some inequalities we're going to treat this as if it's an equation so we're going to pretend this less than or equal to is just an equal to the only time you will change an inequality is if you multiply or divide on the very last step you will flip your inequality and I'll show you when those happen okay so the next thing we're going to do is simplify this so if you have negative 5 minus a negative 9 we have a double negative in the middle so that becomes plus so negative 5x plus 9 is less than or equal to negative 6 now we have a two-step equation so we're gonna subtract 9 and the nines cancel so we have negative 5 to bring down on the left side is less than or equal to a negative 15 same sign you add and keep the sign and now we're gonna divide by negative now this is the step very last step if you divide or multiply by a negative we're gonna turn the inequality the opposite way so it's a less than or equal to you we're going to change it to a greater than or equal to symbol so the 5s cancel and we're left with X is greater than or equal to and then this side negative 15 divided by negative 5 is positive 3 so that's how we work an inequality treat it as if it is an equation and then in the last step if you multiply or divide by negative we flip the inequality okay so let's look at this next one okay we have X divided by negative 6 is greater than equal to 14 we're dividing by negative 6 so we have to multiply by negative 6 now notice we're multiplying by a negative this is the last step of the equation so we are going to have to flip it to a less than or equal to so the six is the negative six is cancel and I have X is less than or equal to because we have the flip and then negative six times 14 is let's see six times four is twenty-four carry the two six times one is six plus 2 more is eight and then a positive times a negative is a negative so there's our answer X is less than or equal to negative 84 okay so let's look at another inequality this is a two-step now I can go ahead and look at this and see that the coefficient in front of X is positive so in this problem I will not have to flip my inequality okay so let's just solve it I'm going to add my 4 to move it to the other side now I'm adding a negative but since I'm not multiplying or dividing I don't have to flip I bring down a 9 I bring down my greater than or equal to the force cancel and I have 9x and it's a positive 9x I bring down then I'm going to divide by 9 so 1 is greater than or equal to X and if you like the X on the left you can take it and flip it if you flip the order the inequality also flips so it's X is less than or equal to 1 so there's that inequality okay now this is our last group of problems let's look at these these are evaluating problems we're going to define a to be negative 5 B to be negative 2 and X to be positive 4 we're going to solve this equation by plugging in values so we have 8 a minus 3 B plus 18 so we're going to plug in and five wherever there's an a a negative to wherever there's a B and a four wherever there's an X well there's not an X so I'm not going to use that this time but we can plug these two values in so I have 8a that means multiplication so eight times negative five minus three times and I'm going to plug in my negative two plus 18 now let's simplify this eight times negative five is negative 40 negative 3 times negative 2 is a positive 6 plus 18 now let's just add left to right negative 40 plus 6 because negative 34 negative 34 plus 18 I subtract and take the sign of the larger so the sign of the larger is actually a negative because negative a negative 34 there's just more negatives and positives so I'm going to have a negative answer and I'm going to subtract so 14 minus 8 is 6 and then 2 minus 1 is 1 so it's negative 16 is my final answer okay now let's look at simplifying all we're going to do is combine like terms so we have groups of X's and groups of Y's and we're going to combine them together so I'm going to underline all my X's so I've got 6 X plus 4 X minus 8 X let's combine just the XS that's gonna give me 10 X minus 8 X which is positive 2 X now let's circle the Y's I have a negative 3y and then negative 2i there are only two terms they're the same sign so I'm gonna add and keep the sign so that's negative 5y now I'm done because I cannot add those two terms together because the variables are different okay now let's look at our last problem we have distributing on the left side or on the the first expert part of the expression and then we actually have another distributing it doesn't look like it but there's a negative one so I'm gonna draw that negative one right there so we can see it and we can see we have to distribute that in so let's start by distributing the 5 we have 5 X minus 20 and then I'm going to distribute the negative 1 so I've got a minus X minus 7 now I can combine my like terms 5x minus X what's 5x minus X that's 4 X and then I have a negative 20 minus 7 they're the same sign so I'm gonna add and keep the sign so that's negative 27 so 4x minus 27 is the last problem I hope this video was helpful on the seventh grade year in review part 2 [Music]