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: 23

Answer

{$\frac{25}{3}$}

Work Step by Step

5x - (2x- 10) = 35 Step 1 : Drop parentheses and change the sign of each term in parentheses: - (2x - 10) = -2x + 10 5x - 2x + 10 = 35 Step 2: Combine like terms 5x - 2x = (5-2)x = 3x 3x + 10 = 35 Step 3: subtract 10 from both the sides 3x +10 - 10 = 35 -10 Step 4: Simplify 3x = 25 Step 5: Divide both the sides by 3 $\frac{3x}{3}$ = $\frac{25}{3}$ Step 6: Simplify x = $\frac{25}{3}$ Now we check the proposed solution, $\frac{25}{3}$, by replacing x with $\frac{25}{3}$ in the original equation. Step 1: the original equation 5x - (2x -10) = 35 Step2: Substitute $\frac{25}{3}$ for x 5. $\frac{25}{3}$ - (2.($\frac{25}{3}$) - 10) = 35 Step 3: Multiply 2. $\frac{25}{3}$= $\frac{50}{3}$. 5. $\frac{25}{3}$ = $\frac{125}{3}$ $\frac{125}{3}$ - ($\frac{50}{3}$ - 10) = 35 Step 4: Solve parenthesis $\frac{50}{3}$ - 10= $\frac{20}{3}$ $\frac{125}{3}$ - $\frac{20}{3}$ = 35 Step 5: Subtract $\frac{105}{3}$ = 35 Step 6 35 = 35 Since the check results in true statement, we conclude that the solution set of the given equation is {$\frac{25}{3}$}
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