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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 =