## Algebra 1

Published by Prentice Hall

# Chapter 2 - Solving Equations - 2-4 Solving Equations with Variables on Both Sides - Practice and Problem-Solving Exercises - Page 106: 22

b = 7

#### Work Step by Step

8 - (3 + b) = b - 9 Use the distributive property: 8 - 1(3) + -1(b) = b - 9 Simplify: 8 - 3 - b = b - 9 To get the variable (b) on one side of the equation, add b to the right side of the equation. This also removes b from the left side of the equation. 8 - 3 - b + b = b - 9 + b Simplify to get: 8 - 3 = 2b - 9 Add 9 to both sides of the equation. 8 - 3 + 9 = 2b - 9 + 9 Simplify to get: 14 = 2b Divide both sides by 2: $\frac{14}{2}$ = $\frac{2b}{2}$ 7 = b Check: To check whether 7 is the correct answer, replace b with 7 in the original equation and solve. 8 - (3 + b) = b - 9 8 - (3 + 7) = 7 - 9 8 - 3 - 7 = 7 - 9 -2 = -2

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