## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 6 - Algebra: Equations and Inequalities - 6.2 Linear Equations in One Variable and Proportions - Exercise Set 6.2: 47

{1}

#### Work Step by Step

$\frac{x}{3}$ + $\frac{x}{2}$ =$\frac{5}{6}$ Step 1 : Multiply both the sides by 6 ($\frac{x}{3}$ + $\frac{x}{2}$)* 6 =$\frac{5}{6}$ * 6 Solve $\frac{x}{3}$ * 6 + $\frac{x}{2}$ * 6=$\frac{5}{6}$*6 2x + 3x = 5 Step 2 : Add 2x +3x = (2+3)x = 5x 5x = 5 Step 3: Divide both the sides by 5 $\frac{5x}{5}$ = $\frac{5}{5}$ x = 1 Now we check the proposed solution, 1 , by replacing x with 1 in the original equation. Step 1: the original equation $\frac{x}{3}$ + $\frac{x}{2}$ =$\frac{5}{6}$ Step2: Substitute 1 for x $\frac{1}{3}$ + $\frac{1}{2}$ =$\frac{5}{6}$ Step 3: Multiply both sides by 6 $\frac{1}{3}$*6 + $\frac{1}{2}$*6 =$\frac{5}{6}$*6 Simplify 2+3 = 5 Step 4 : Add 2+3 = 5 5 = 5 Since the check results in true statement, we conclude that the solution set of the given equation is {1}.

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