### Concept (1)

To solve an absolute value inequality, knowledge of absolute values and solving inequalities are necessary. Absolute value inequalities can have one or two variables. Solving and graphing absolute value inequalities with two variables is also a skill that math teachers require students to master in Algebra I.

### Sample Problems (7)

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Solve for x. Graph your solution.

3|x − 2| > 15
###### Problem 1
How to solve and graph absolute value inequalities with one variable when there is a compound solution.

Solve for x. Graph your solution.

4 − |2x − 6| ≤ 8
###### Problem 2
How to solve and graph absolute value inequalities with one variable when there is a infinite solution.

Write an absolute value inequality for

-3 ≥ x ≤ 3
###### Problem 3
How to write the absolute value inequality when provided with a graph.
###### Problem 4
Solving absolute value inequalities with changing the inequality sign direction and +, - value.
###### Problem 5
Special cases of absolute value inequalities where the equation is greater than or less than a negative value.
###### Problem 6
Solving absolute value inequalities and determining whether to use "and" or "or" in the solution.
###### Problem 7
Special cases of no real solutions or all real numbers in solving absolute value inequalities.