# Compound inequalities

### Compound inequalities

#### Lessons

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.

• Introduction
Introduction to compound inequalities

i. Recap of inequalities symbols

ii. Ideas of AND and OR

• 1.
Evaluate Compound Inequalities: OR

Solve the following compound inequalities:

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

• 2.
Solve the following compound inequalities:

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

• 3.
Evaluate Compound Inequalities: AND

Solve the following compound inequalities:

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

• 4.
Solve the following compound inequalities:

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

• 5.
Analyze the Alternate Form of Compound Inequalities: AND

Solve the following compound inequalities:

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

• 6.
Solve the following compound inequalities:

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

• 7.
Special Cases: No solution, All Real Numbers

Solve the following compound inequalities:

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

• 8.
Solve the following compound inequalities:

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