5.7 Starting a Two-Step Equation

Introduction

Unit 1

Unit 2

Unit 3

Unit 4

Unit 5

Unit 6

Math Basics  >  Unit 5 Equations  >  Lesson 5.7 Starting a Two-Step Equation

Video Lesson

Click play to watch the video and answer the questions for points!

Practice Activity

For each equation, click on the number that we need to "undo" first.

+ Video Transcript

In our last lesson, we looked at solving one-step equations, meaning there was only one number that we needed to undo to get our variable isolated. Now we're going to look at solving two-step equations. So the challenge is when there's two numbers that we need to undo, where do we begin? Here is an example. We have two x minus eight equals 34. I'm going to draw a line through the equal sign so we can see the left and right sides of the equation clearly. And we can see our variable. X is on the left side. We have the two that's being multiplied by the x. Then we have the eight that's being subtracted. Well, that's two numbers that we need to undo to get x by itself. Which number do we undo first? To figure this out, we're going to revisit our old friend PEMDAS, the order of operations. Except instead of following the order of operations from beginning to end like we normally do, we're actually going to follow the order of operations in reverse. Think of solving equations as an undoing process. We have to do everything backwards to get down to x. So that means that we'll start by undoing addition and subtraction first, then work our way up to multiplication and division, and then exponents and then parentheses if we have those. Well, in this equation, we have the two that's being multiplied. So we have multiplication and then we have subtraction. Because the eight is being subtracted, this means that we would start by undoing the subtraction first that's at the bottom of our order of operations. So since eight is subtracted, we would undo the eight first. With this one, we have x over seven. Now remember, fraction represents division. So we can say this is x divided by seven. Then we have plus three equals five. I can see that x is on the left side of the equation again. And I have two numbers that I need to undo to get x by itself. I have the seven and the three. Which one do we undo first? We follow our order of operations, but in reverse. So the seven is being divided. We have x divided by seven. So that will get done during the division step. And then we have addition as we see plus three. Since the three goes along with addition and we undo addition and subtraction first, that means that we would start there when we want to isolate x. And then once the three is undone, we would move on to the seven. We're going to go on to our next lesson to figure out exactly how to finish solving these equations.

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