### Concept (1)

In mathematics, it can be useful limit the solution or even have multiple solutions for an inequality. For this we use compound inequalities, inequalities with multiple inequality signs. When solving compound inequalities, we use some of the same methods used in solving multi-step inequalities. The solutions to compound inequalities can be graphed on a number line, and can be expressed as intervals.

### Sample Problems (8)

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Solve and graph the solution.

-5 ≤ 2x + 3 < 11
###### Problem 2
How to solve and graph compound inequalities with two inequality signs or an "and."

Solve and graph the solution.

3 + x < 11 or x + 2 > 18
###### Problem 3
How to solve and graph compound inequalities with an "or."
###### Problem 4
Interpreting special cases of compound inequalities, including no solution and all reals
###### Problem 5
Solving and graphing compound inequalities with one variable using interval notation
###### Problem 6
Splitting a compound inequality with two < signs into two separate inequalities connected by the word "and"
###### Problem 7
Solving a compound inequality with two < signs in the same line
###### Problem 8
Solving and graphing "or" compound inequalities with one variable
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