Lesson 11: Solving for a Variable on One Side Using Multiplication, Addition, and Subtraction #6

[One speaker]

[A white screen with the words, “Solve for the variable: -5q - 29 = 41” written at the top.]

Instructor: Solve for the variable. So we are going to isolate Q right here and try to get it all by itself on one side of the equals sign--one side of the equation. So to do that, we have to start. We kind of do reverse order of operations. We got to get rid of our addition and subtraction first. So we’re going to use the additive inverse of negative twenty-nine, which is positive twenty-nine. So we’re going to add twenty-nine to both sides. And remember that whatever we do to one side, we have to do to the other because of our equal sign. We want to keep those two sides equal. And so that leaves us with--we have a negative five times Q. And then negative twenty-nine plus twenty-nine is zero. So we can get rid of that there, and that equals forty-one plus twenty-nine, which is seventy.

[writes “-5q = 70”]

Now we are still trying to isolate our Q, so we’re going to use the multiplicative inverse of negative five. If we have ⅕, we can see that our fives will cancel, but that would leave us with a negative one times Q, and so we need a negative ⅕ because a negative times a negative is a positive. [writes “(⅕)” in front of the equation] And what we do to one side, we have to do to the other. So we’re going to multiply by a negative ⅕ over here. [adds to the equation which now reads, “(-⅕) -5q = 70(-⅕)”] Now we can see that our five’s cancel, and a negative times a negative is positive, and we are left with just Q. Then on the right side of the equation, we have seventy, which we can write as seventy over one, times a negative ⅕. [writes “q = 70/1 x -⅕ = -70/5 = -14”] Seventy times a negative one is negative seventy, and one times five is five.

And now, negative seventy over five is the same thing as negative seventy divided by five, and so that leaves us with a negative fourteen. But now we can check our answer. So we found that Q is equal to negative fourteen. [writes “q = -14”] But we can plug this back into our equation--whoops--right here and see if we have the right answer. And if we find that this side equals this side, then we know we have the right answer. If not, we have to start over, but let’s try. We have negative five times negative fourteen, right? We had Q up here, but we found Q to be negative fourteen, so we’re going to plug that in and see what we get. [writes “-5(-14) - 29 = 41”] Minus twenty-nine equals forty-one. And negative five times negative fourteen is seventy. So we have seventy minus twenty-nine equals forty-one. [writes “70 - 29 = 41”] And yes, seventy minus twenty-nine does equal forty-one, so we have the right answer.

[End of Video]