Chapter 17

Making Inequalities More Fair

An inequality is a statement involving more than one expression and/or number. When two expressions are set greater than or less than one another, you want to determine for what numbers the statement is true. Inequalities can also involve several statements, one greater than the next, greater than the next, and so on. Solving these statements involves treating each section exactly the same and using the rules for dealing with inequalities.

The Problems You'll Work On

In short, here's what you'll be doing in this chapter:

What to Watch Out For

As you zip through the problems in this chapter, keep the following in mind:

Performing Operations on Inequalities

716–719 Perform the indicated operation on the inequalities.

716. Starting with 7 > 3, add −2 to each side, and then multiply each side by −4.

717. Starting with −4 < 1, multiply each side by −2, and then subtract 3 from each side.

718. Starting with −6 ≤ 6, divide each side by −3, and then add 3 to each side of the equation.

719. Starting with 0 ≥ −4, add 3 to each side of the equation and then multiply each side by −1.

Writing Inequalities Using Interval Notation

720–723 Change the inequality notation to interval notation.

720. −3 ≤ x < 2

721. 0 ≤ x ≤ 4

722. x > −3

723. x ≤ 7

Changing Interval Notation to Inequality Notation

724–727 Change the interval notation to inequality notation.

724. [−6, ∞)

725. (−∞, −2)

726. [−4, 7)

727. (2, 3)

Solving Linear Inequalities

728–733 Solve each linear inequality for the values of the variable.

728. 2x − 5 < 3

729. 3x − 2 ≥ 4x + 3

730. −3(x + 7) ≤ 2x + 9

731.

732.

733.

Taking on Compound Inequalities

734–737 Solve each compound inequality

734. −5 ≤ 3x + 1 < 7

735. −4 < 6 − 5x < 11

736.

737. −15 < −3(3 − 2x) < −9

Solving Quadratic Inequalities

738–745 Solve each quadratic inequality using a number line.

738. (x − 3)(x + 4) < 0

739. (2x + 5)(x + 8) ≥ 0

740. x² − 8x − 9 ≤ 0

741. x² − 4x − 21 > 0

742. 48 − x² > −2x

743. 36 − x² ≤ 0

744. 5x² < 15x

745. x² + 4x + 4 ≥ 0

Finding Solutions of Nonlinear Inequalities

746–753 Solve each nonlinear inequality using a number line.

746. x(x + 3)(x − 2) > 0

747. (x + 1)²(x + 5)(x − 7) ≤ 0

748. x³ + x² − 36x − 36 ≥ 0

749. x³ − 2x² + x < 0

750.

751.

752.

753.

Rewriting and Solving Absolute Value Inequalities

754–761 Solve the absolute value inequalities by rewriting the statements.

754. |3x + 2| ≥ 7

755. |4 − x| < 6

756. 5|2x + 1| ≤ 20

757.

758. |x + 4| − 5 > 3

759. |5 − 2x| + 4 ≤ 7

760. 2|x − 5| − 4 ≥ −2

761.

Delving into Complex Inequalities

762–765 Solve the complex inequalities.

762. −4 < 3x + 2 ≤ 2x + 3

763.

764. −5 < 4x − 1 < 6x + 7

765. x + 1 ≤ 3x + 5 < 8