## Algebra 1

Published by Prentice Hall

# Chapter 3 - Solving Inequalities - 3-6 Compound Inequalities - Practice and Problem-Solving Exercises - Page 204: 9

#### Answer

$-5\lt x\lt7$

#### Work Step by Step

If x is between -5 and 7, then x must be greater than -5 and less than 7. The phrase between does not imply that the endpoints are part of the solution set, so the endpoints on the number line are open circles, and the inequality operators do not include "or equal to." The compound inequality could be written as: $x\gt-5$ and $x\lt7$ It is typical to reverse one of the inequalities so that the same operator is used in both: $x\gt-5\ and\ x\lt7$ becomes $-5\lt x\ and\ x\lt7$ which becomes $-5\lt x\lt7$

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