91Ó°ÊÓ

The _______ ______ of a number is its distance from 0 on a number line.

Fill in the blanks. We read the set- _____ notation \(\\{x | x<1\\}\) as "the set of all real numbers \(x\) _____ _____ \(x\) is less than \(1 . "\)

Fill in the blanks. To _____ an inequality means to find all values of the variable that make the inequality true.

a. To graph the inequality \(y>3 x-1\), we begin by graphing the boundary line \(y=3 x-1 .\) What is the slope \(m\) of the line? What is its \(y\) -intercept? b. To graph the inequality \(2 x+3 y \leq-6,\) we begin by graphing the boundary line \(2 x+3 y=-6 .\) What are its \(x\) - and \(y\) -intercepts?

Fill in the blanks. a. When solving a compound inequality containing the word and, the solution set is the _________ of the solution sets of the inequalities. b. When solving a compound inequality containing the word or, the solution set is the _________ of the solution sets of the inequalities.

Complete the solution to solve the inequality. Fill in the blank: \(\infty\) is a symbol representing positive _____.

Graph the solution set of each system of inequalities. See Example 2 . $$\left\\{\begin{array}{l}2 x+y \leq 2 \\\y \geq x \\\x \geq 0\end{array}\right.$$

a. Graph: \((-\infty, 2) \cup[3, \infty)\) b. Graph: \((-\infty, 3) \cap[-2, \infty)\)

Graph the solution set of each system of inequalities on a rectangular coordinate system. $$\left\\{\begin{array}{l}2 x<3 y \\\2 x+3 y \geq 12\end{array}\right.$$

Solve each inequality. Graph the solution set and write it using interval notation. See Example 2. $$ x-5>2 $$