Chapter 13: Two-Step Equations

Adapted from Wentworth's Elementary Algebra for MathDoctor.net

13.1 Working Backward

In Chapter 8, we learned PEMDAS to solve expressions. When solving an equation, we are taking the expression apart. This means we usually work in Reverse PEMDAS (SADMEP).

The Strategy: Undo Subtraction/Addition first,
then undo Division/Multiplication.

13.2 The Step-by-Step Method

Let's solve: 2x + 5 = 13

1 Undo Addition: Subtract 5 from both sides.
2x + 5 - 5 = 13 - 5
2x = 8

2 Undo Multiplication: Divide both sides by 2.
2x / 2 = 8 / 2
x = 4

13.3 Checking Your Work

One of the best things about Algebra is that you never have to wonder if you got the right answer. Just plug your result back into the original equation.

Check: Does 2(4) + 5 = 13?
8 + 5 = 13. Yes!

Chapter 13 Review

Solve for the variable and check your answer:

3x - 4 = 11
5y + 10 = 50
x / 2 - 3 = 7
10 - 2a = 4
(Hint: Be careful with the negative sign on the 2a!)

Chapter 13 Exercises

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Doctor's Recommendation: A Second Opinion

Two-step equations add a layer of complexity. If you need a break from the 1906 logic of Wentworth, we recommend the "Big Fat Notebook" for Algebra 1. It offers a colorful, highly simplified second perspective that perfectly complements our modernization of this classic text.

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