## Algebra 2 Common Core

Published by Prentice Hall

# Chapter 1 - Expressions, Equations, and Inequalities - 1-5 Solving Inequalities - Practice and Problem-Solving Exercises - Page 38: 41

#### Answer

$x \ge 1 \text{ or } x < 6$ The solution is $\left\{x| x\text{ is a real number}\right\}$ Refer to the graph below. #### Work Step by Step

Solve each inequality: \begin{align*} 3x &\ge 3\\\\ \frac{3x}{3} &\ge \frac{3}{3}\\\\ x &\ge 1 \end{align*} $$\text{or}$$ \begin{align*} 9x&\lt 54\\\\ \frac{9x}{9} &\lt \frac{54}{9}\\\\ x&\lt 6 \end{align*} Graph each inequality to obtain the one in the attached image below. Since the compound inequality involves the conjunction $\text{OR}$, then the solutions to the inequality are the combined numbers of the two graphs. Notice the when combined, the entire number line is covered. Thus, the solution is $\left\{x|x \text{ is a real number}\right\}$. After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.