Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.7 Inequalities - 1.7 Exercises - Page 159: 20


$\color{blue}{\left(-\infty, \dfrac{15}{7}\right)}$

Work Step by Step

Distribute $5$ and $-6$ to obtain: $2-4x+5(x) -5(1)\lt -6(x)-(-6)(2) \\2-4x+5x-5 \lt -6x -(-12) \\x-3 \lt -6x+12$ Add $6x$ and $3$ to both sides, then combine like terms to obtain: $x-3 +6x+3 \lt -6x+12+6x+3 \\7x \lt 15$ Divide $7$ to both sides of thee equation to obtain: $\dfrac{7x}{7} \lt \dfrac{15}{7} \\x \lt \dfrac{15}{7}$ Thus , the solution set is: $\color{blue}{\left(-\infty, \dfrac{15}{7}\right)}$
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