1.5 Solving Inequalities

Honors Algebra II

Properties of Inequalities, page 34Property  Let a, b, and c represent real numbers.

                                                                                                                                                                                                                                   

***If you multiply or divide by a negative number, FLIP the inequality sign!***

THE BIG REMINDER!

Solving Inequalities Example

Solve -5[2 – (1 + b)] ≥ 25 + 7(2b – 3)

Solving Inequalities Example

CHECK: -5[2 – (1 + b)] ≥ 25 + 7(2b – 3)

Solving Inequalities – Special Case

Example: Solve 2x – 3 > 2(x – 5)

Solving Inequalities – Special Case

Example: Solve 7x + 6 < 7(x – 4)

Compound Inequalities

More than one restriction on the variable.

Joined by AND or OR

And Intersection BOTH parts must be true looking for overlap

Or Union EITHER part must be true no overlap is needed

Compound Inequalities AND

Solve 3x – 1 > -28 and 2x + 7 < 19

Exceptions

Solve 3x + 6 < -9 and 2x + 1 > 9

Compound Inequalities OR

Solve 4y – 2 ≥ 14 or 3y – 4 ≤ -13

Exceptions

2x + 3 ≥ 5 or 3x – 9 < 6