Pre-Calculus 11 Absolute Value Inequalities

Lesson Focus: To solve an absolute value inequality algebraically; to graph the solution of an absolute value

inequality on a number line.

an absolute value inequality is an inequality that has a variable within the absolute value symbol

e.g. 53 x

in order to solve these inequalities:

1) change the absolute value symbol for round brackets and add a in front of the brackets

2) solve both inequalities

3) graph the solution on a number line

do not forget to “flip” the inequality when you multiply or divide by a negative

e.g. Solve the following inequalities. Graph the solution on a number line.

1. 84 x 2. 61 x

NOTE: or will always produce an inequality that has two parts (use two separate rays) while or

will always produce an inequality that is a segment of the number line (use combined notation)

inequalities that involve two absolute values (with or without a constant) should always be graphed

use your graphing calculator to graph the absolute value inequality

always make the larger side of the inequality the THICKER line

determine the x-values where the thicker line is ABOVE the thin line for the solution to the inequality

in order to find the critical points of the inequality, use the:

1. INTERSECT feature (2nd

/TRACE/5) when your inequality has the form Y1 > Y2

2. ZERO feature (2nd

/TRACE/2) when your inequality has the form Y1 > 0

e.g. Graph the following inequalities on your graphing calculator. Sketch the graph on the window

provided. Determine the solution of the inequality. Graph your answer on a number line.

1. 423 xx Y1 =

Y2 =

2. 842 xx Y1 =

Y2 =

3. 053 xx Y1 =

Y2 =