1. Equations & Inequalities

Solve each absolute value inequality. 5|2x + 1| - 3 ≥ 9

In Exercises 59–94, solve each absolute value inequality. - 2|x - 4| ≥ - 4

Solve each absolute value inequality. - 4|1 - x| < - 16

To see how to solve an equation that involves the absolute value of a quadratic polynomial, such as | x² - x | = 6, work Exercises 83–86 in order. For x² - x to have an absolute value equal to 6, what are the two possible values that x may assume? (Hint: One is positive and the other is negative.)

Solve each inequality. Give the solution set using interval notation.

$11x\ge 2(x-4)$

In Exercises 59–94, solve each absolute value inequality. 3 ≤ |2x - 1|

Solve each inequality. Give the solution set using interval notation. -5x - 4≥3(2x-5)

Solve each inequality. Give the solution set using interval notation.

$7x-2(x-3)\le 5(2-x)$

Use the method described in Exercises 83–86, if applicable, and properties of absolute value to solve each equation or inequality. (Hint: Exercises 99 and 100 can be solved by inspection.) | 3x² + x | = 14

Solve each inequality. Give the solution set using interval notation. 5 ≤ 2x -3 ≤ 7

In Exercises 59–94, solve each absolute value inequality. 5 > |4 - x|

Solve each inequality. Give the solution set using interval notation.

$-8>3x-5>-12$

In Exercises 59–94, solve each absolute value inequality. 1 < |2 - 3x|

In Exercises 59–94, solve each absolute value inequality. $12 < \left| -2x + \frac{6}{7} \right| + \frac{3}{7}$

Solve each absolute value inequality. 4 + |3 - x/3| ≥ 9