# compound inequalities

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### Compound Inequalities:

Compound Inequalities Algebra - I

### Review:

Review Steps in solving an inequality are the same as solving an equation: 1 . Get on one level (if negative, flip sign for inequalities) 2. Get rid of groupings – use the distributive property 3. Combine like terms – including constants 4. Get variables on the same side 5. Get rid of addition and subtraction by using inverse operation 6. Get rid of multiplication and division by using inverse operation **If you multiply or divide by a negative on both sides, then you must flip the inequality sign.** 7. Get rid of exponents

### Compound Inequalities:

Compound Inequalities Compound inequalities are inequalities which contain “and” or ”or” Ex. x ≥ -5 and x ≤ 7 can also be written as -5 ≤ x ≤ 7 Ex. Numbers that are at least -2 and at most 4 can also be written -2 ≤ x ≤ 4 Ex. All real numbers that are less than -3 or greater than 7 x < -3 or x > 7

### Compound Inequalities:

Compound Inequalities To solve an “and” compound inequality – split it into two separate problems -4 < x – 5 ≤ - 1 -4 < x-5 and x-5 ≤ - 1 +5 +5 1 < x and +5 +5 x ≤ 4 1 < x ≤ 4

### Compound Inequalities:

Compound Inequalities Solve an “or” compound inequality by solving each inequality separately . 4x + 3 < -5 OR -2x + 7 < 1 -3 -3 - 7 -7 4x < -8 -2x < -6 4 4 -2 -2 x < -2 OR x > 3 Therefore, the numbers smaller than -2 or larger than 3 solve this inequality. You can choose a number and test it out.