1. Equations & Inequalities

Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (x - 2)/(x + 2) ≤ 2

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | > 7

Solve each rational inequality. Give the solution set in interval notation. (x-3)/(x+5)≤0

Answer the following. Why can 3 not be in the solution set of 14x+9 / x-3 < 0? (Do not solve the inequality.)

Match the inequality in each exercise in Column I with its equivalent interval notation in Column II. 6≤x

In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 3x - 7 ≥ 13

In Exercises 73–74, use the graph of the rational function to solve each inequality.

1/4(x + 2) ≤ - 3/4(x - 2)

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. $2x^2+3x>0$

In Exercises 71–72, use the graph of the polynomial function to solve each inequality.

$2x^3+11x^2\ge 7x+6$

Solve each rational inequality. Give the solution set in interval notation. (5-3x)²/(2x-5)³>0

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

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

In Exercises 59–94, solve each absolute value inequality. |x + 3| ≤ 4

Solve each inequality. Give the solution set using interval notation. 3x+6 / x-5 > 0