Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 2 - Section 2.5 - Compound Inequalities - Exercise Set: 63

Answer

The solution is $(-\infty,1]\cup\Big(\dfrac{29}{7},\infty\Big)$

Work Step by Step

$3x+2\le5$ or $7x\gt29$ Solve the first inequality: $3x+2\le5$ Take $2$ to the right side: $3x\le5-2$ $3x\le3$ Take $3$ to divide the right side: $x\le\dfrac{3}{3}$ $x\le1$ Expressing the solution in interval notation: $(-\infty,1]$ Solve the second inequality: $7x\gt29$ Take $7$ to divide the right side: $x\gt\dfrac{29}{7}$ Expressing the solution in interval notation: $\Big(\dfrac{29}{7},\infty\Big)$ Since the compound inequality is formed by the word "or", the solution is composed by the solutions of both inequalities: The solution is $(-\infty,1]\cup\Big(\dfrac{29}{7},\infty\Big)$
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