# Compound inequalities

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##### Intros
###### Lessons
1. Introduction to compound inequalities

i. Recap of inequalities symbols

ii. Ideas of AND and OR

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##### Examples
###### Lessons
1. Evaluate Compound Inequalities: OR

Solve the following compound inequalities:

$4x - 16$ < $16\;$ OR $\;8x + 15 \leq -1$

1. Solve the following compound inequalities:

$4x + 5$ < $13\;$ OR $\;3x$ > $39$

1. Evaluate Compound Inequalities: AND

Solve the following compound inequalities:

$4x + 30$ > $34\;$ AND $\;12x - 6$ > $18$

1. Solve the following compound inequalities:

$-6x + 2$ > $20\;$ AND $\;13x + 11 \leq 50$

1. Analyze the Alternate Form of Compound Inequalities: AND

Solve the following compound inequalities:

$-5 \leq 3x + 1 \leq 7$

1. Solve the following compound inequalities:

$-14$ < $1 - 5x \leq 11$

1. Special Cases: No solution, All Real Numbers

Solve the following compound inequalities:

$3x - 3$ < $9\;$ AND $\;6x + 1$ > $37$

1. Solve the following compound inequalities:

$5x + 6$ < $36\;$ OR $\;-3x \leq 18$

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##### Practice
###### Topic Notes

If the relationship between the compound inequalities is OR and they point towards the same direction, you will pick the inequality which has a broader range.

If the relationship between the compound inequalities is AND and they point towards the same direction, you will pick the inequality which has a narrower range.

When you multiply or divide a negative number, the inequality symbol will be reversed.