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: 22

Answer

{$\frac{5}{3}$}

Work Step by Step

10(3x + 2) = 70 Step 1 : Use distributive property 10.3x + 10.2 = 70 Step 2: Multiply 10.3x = 30x, 10.2 = 20 30x + 20 = 70 Step 1: subtract 20 from both the sides 30x + 20 - 20 = 70 - 20 Step 2: Simplify 30x = 50 Step 3: Divide both the sides by 30 $\frac{30x}{30}$ = $\frac{50}{30}$ Step 4: Simplify x = $\frac{5}{3}$ Now we check the proposed solution, $\frac{5}{3}$, by replacing x with $\frac{5}{3}$ in the original equation. Step 1: the original equation 10(3x + 2) = 70 Step2: Substitute $\frac{5}{3}$ for x 10(3.($\frac{5}{3}$) + 2) = 70 Step 3: Multiply 3, $\frac{5}{3}$= 5 10(5+2) = 70 Step 4: Solve parenthesis 5+2 = 7 10(7) =70 Step 5: Multiply 10.7 = 70 70 = 70 Since the check results in true statement, we conclude that the solution set of the given equation is {$\frac{5}{3}$}
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