ALGEBRA II HONORS/GIFTED - SECTION 1-5 (Solving Inequalities) @ SECTION 1-5 : SOLVING INEQUALITIES

Human Number Line activity. INEQUALITY : A mathematical sentence such that the sides are not equal. Inequalities use one or more of the symbols : . Compound inequalities are composed of two or more inequalities. 1) How many solutions can an inequality have? None, one, infinite! 2) Given 6 < 8, let’s do some… a) adding c) multiplying b) subtracting d) dividing

When you multiply or divide an inequality by a negative number, remember to switch the direction of the inequality.

Solve and graph on a number line. 3) 3x – 5 < 16 {real numbers} will always be the solution set. +5 +5 3x < 21 3 3 7 x < 7 < >

4) +5 +5 -4 • • -4 j > 16 16

5) x – 3 < -2 or x + 3 > 6 How many parts of an “or” statement must be true for the entire statement to be true? +3 +3 -3 -3 x < 1 or x > 3 Just 1 3 This is a compound inequality because it involves two or more inequalities. As long as either part is true, GRAPH IT! So, what is graphed on the number line? 6) 2x – 7 < -11 or -3x + 5 < 3 Both parts!

7) 3 < 2x + 5 < 11 Means 3 < 2x + 5 and 2x + 5 < 11. Solving this compound inequality in this format gets kind of tricky. Let’s do something different – something us middle children will love! Solve for x in the middle. -5 -5 -5 -2 < 2x < 6 2 2 2 -1 < x < 3 -1 3 So, where is x located? Yep, in the middle! So, graph, yep, in the middle.

8) 5 > -3x + 2 > -4 smaller # < x < larger # larger # > x > smaller #