Algebra 1
Name: _______________________________
Unit 1: L4
Date: _________________ Period: _______
Absolute Value Inequalities (6.4)
Essential Questions:
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Is there only one correct sequence of steps for solving an inequality?
Why should you check a solution?
Are inequalities solved the same way as equations?
How do you check a solution of an inequality?
Goal:
 I can solve and graph absolute value inequalities.
Steps:
1) Isolate the absolute value expression
2) Determine if the absolute value inequality is an “and” or an “or” problem
a) “AND”  “Less th AND”
3)
4)
5)
6)
b) “OR”  “Great OR”
Set-up two inequalities
a) For the 1st inequality, drop the absolute value bars and solve.
b) For the 2nd equation, drop the bars, negate the opposite side, and flip the inequality sign
Solve both inequalities
Check… Always back into the “original” problem.
Graph your solution on a number line
Section 1: ISOLATED… Solve and check the absolute value equation.
1) x  4  3
YT 1)
x6 8
Answer:
Answer:
Graph:
Graph:
Section 2: NOT ISOLATED… Solve and check the absolute value equation.
2) 2 x  1  3  6
YT 2) 2a  5  2  7
Answer:
Answer:
Graph:
Graph:
Section 3: SPECIAL CASES… Solve and check the absolute value equation.
3) 4 y  2  2
YT 3)
Answer:
Answer:
4)  3 a  1  9
Answer:
x 6 8  3
YT 4) 
2
m  9  10
3
Answer:
Homework: Pg. 357 # 41-59 odd (graph answers on number line)
Ticket Out / Lesson summary:
How do you determine if the absolute value inequality is an “and” or an “or” problem?