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 - Page 95: 65


This compound inequality has $\textbf{no solution}$.

Work Step by Step

$5-x\gt7$ and $2x+3\ge13$ Solve the first inequality: $5-x\gt7$ Take $x$ to the right side and $7$ to the left side: $5-7\gt x$ $-2\gt x$ Rearrange: $x\lt-2$ Expressing the solution in interval notation: $(-\infty,-2)$ Solve the second inequality: $2x+3\ge13$ Take $3$ to the right side: $2x\ge13-3$ $2x\ge10$ Take $2$ to divide the right side: $x\ge\dfrac{10}{2}$ $x\ge5$ Expressing the solution in interval notation: $[5,\infty)$ Since the compound inequality is formed by the word "and", the solution is composed by the numbers that satisfy both inequalities simultaneously. The solution would be $(-\infty,-2)\cap[5,\infty)$, but since these two intervals have no elements in common, this compound inequality has no solution.
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