Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 6 - Algebra: Equations and Inequalities - 6.2 Linear Equations in One Variable and Proportions - Exercise Set 6.2: 33

Answer

{-$\frac{1}{5}$}

Work Step by Step

2(4 - 3x) = 2(2x + 5) Step 1 : Use distributive property 2.4- 2.(3x) = 2.(2x) + 2.5 simplify 8 - 6x = 4x +10 Step 2 : Collect variable terms on one side and constants on the other side. subtract 4x from both the sides 8 - 6x - 4x = 4x + 10 -4x Simplify 8 - 10x = 10 subtract 8 from both the sides 8 - 10x - 8 = 10 -8 Simplify -10x = 2 Divide both the sides by -10 $\frac{-10x}{-10}$ = $\frac{2}{-10}$ x = $\frac{1}{-5}$ Now we check the proposed solution, -$\frac{1}{5}$ , by replacing x with -$\frac{1}{5}$ in the original equation. Step 1: the original equation 2(4 - 3x) = 2(2x + 5) Step2: Substitute -$\frac{1}{5}$ for x 2(4 - 3 .-$\frac{1}{5}$) = 2(2. -$\frac{1}{5}$ + 5) Step 3: Multiply 3 .-$\frac{1}{5}$ = -$\frac{3}{5}$, 2. -$\frac{1}{5}$ = -$\frac{2}{5}$ 2(4 + $\frac{3}{5}$) = 2(-$\frac{2}{5}$ + 5 ) Step 4: Solve 2($\frac{23}{5}$) = 2($\frac{23}{5}$) $\frac{46}{5}$ = $\frac{46}{5}$ Since the check results in true statement, we conclude that the solution set of the given equation is {-$\frac{1}{5}$}
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