# Lesson 3-5 Objectives The student will be able to: 1. solve compound inequalities. 2.graph the solution sets of compound inequalities. Designed by Skip.

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Lesson 3-5 Objectives The student will be able to: 1. solve compound inequalities. 2.graph the solution sets of compound inequalities. Designed by Skip Tyler, Varina High School

--A compound inequality is when you SMUSH two inequalities together. --There are two types of compound inequalities: 1. AND - TODAY 2.OR - TOMORROW Designed by Skip Tyler, Varina High School

What is the difference between and and or ? AND means intersection -what the two items have in common OR means union -some answers are in one circle, some answers are in the other…none in the middle AB AB

Let’s look at some AND problems…intersection! AB

1) Graph x < 4 and x ≥ 2 342 ● a) Graph x < 4 b) Graph x ≥ 2 342 o c) Combine the graphs ● 342 o d) Where do they intersect? ● 342 o

2) Which inequalities describe the following graph? -2-3 o o Answer Now 1.y > -3 or y < -1 2.y > -3 and y < -1 3.y ≤ -3 or y ≥ -1 4.y ≥ -3 and y ≤ -1

When written this way, it is the same thing as 6 < m AND m < 8 It can be rewritten as m > 6 and m < 8 and graphed as previously shown, however, it is easier to graph everything between 6 and 8! 3) Graph the compound inequality 6 < m < 8 786 o o

4) Which is equivalent to -3 < y < 5? 1.y > -3 or y < 5 2.y > -3 and y < 5 3.y 5 4.y 5 Answer Now

5) Which is equivalent to x > -5 and x ≤ 1? 1.-5 < x ≤ 1 2.-5 > x ≥ 1 3.-5 > x ≤ 1 4.-5 < x ≥ 1 Answer Now

6) Graph 3 < 2m – 1 < 9 05 -5 + 1 +1 +1 4 < 2m < 10 /2 /2 /2 2 < m < 5

7) Graph -16 < -3x + 8 < -7 Remember, it can also look like this sometimes! -16 < -3x + 8 AND -3x + 8 < -7 0 8 5 -8 -8 -8 -24 < -3x < -15 8 > x > 5 /-3 /-3 /-3 FLIP THE SIGNS!!! 5 < x < 8

8) 2x < -6 and 3x ≥ 12 1.Solve each inequality for x 2.Graph each inequality 3.Combine the graphs 4.Where do they intersect? 5.They do not! x cannot be greater than or equal to 4 and less than -3 No Solution!! -30-6 o -30-6 o 471 o ● 471 o ●

Now…let’s try some AND problems on your clickers!

Remember from yesterday… What is the difference between and and or ? AND means intersection -what the two items have in common OR means union -some answers are in one circle, some answers are in the other…none in the middle AB AB

Let’s look at some OR problems…different directions! AB

9) Graph x < 2 or x ≥ 4 342 ● a) Graph x < 2 b) Graph x ≥ 4 342 o c) Combine the graphs 342 o 342 ●

10) Graph x < 2 or x ≥ 4 05 -5

11) Graph x ≥ -1 or x ≤ 3 The whole line is shaded!! Weird, huh?!

11) Graph 2m – 1 9 Remember, solve each inequality as a separate problem then graph it on the same number line. 2m – 1 9 Graph the direction of m 5. 05 -5

12) Graph -3n 10 Remember, solve each inequality as a separate problem then graph it on the same number line. -3n 10 Graph the direction of n 3. 0 3 -5

Let’s try some OR problems on the clickers!

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