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: 45

Answer

{18}

Work Step by Step

$\frac{2x}{3}$ - 5 =7 Step 1 : Multiply both the sides by 3 ($\frac{2x}{3}$ - 5 ).3=7.3 Solve $\frac{2x}{3}$ .3 - 5.3 =21 2x -15 = 21 Step 2 : Collect variable terms on one side and constants on the other side. add 15 on both the sides 2x -15 + 15 = 21 + 15 2x = 36 Step 3: Divide both the sides by 2 $\frac{2x}{2}$ = $\frac{36}{2}$ x = 18 Now we check the proposed solution, 18 , by replacing x with 18 in the original equation. Step 1: the original equation $\frac{2x}{3}$ - 5 =7 Step2: Substitute 18 for x $\frac{2. 18}{3}$ - 5 =7 Step 3: Simplify $\frac{36}{3}$ - 5 =7 Step 4 : Divide $\frac{36}{3}$ = 12 12 -5 = 7 Solve 7 = 7 Since the check results in true statement, we conclude that the solution set of the given equation is {18}
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