Objectives The student will be able to: 1. solve compound inequalities. 2. graph the solution sets of compound inequalities.

What is the difference between and and or? AND means intersection -what do the two items have in common? OR means union -if it is in one item, it is in the solution A B

Some vocabulary…. A compound inequality consist of two separate inequalities joined by and or or. The graph of a compound inequality with and is the intersection of the graph of inequalities. The graph of a compound inequality with or is the union of the graphs of the inequalities.

● ● ● 1) Graph x < 4 and x ≥ 2 a) Graph x < 4 o o b) Graph x ≥ 2 3 4 2 o 3 4 2 o b) Graph x ≥ 2 3 4 2 ● ● c) Combine the graphs d) Where do they intersect? ● 3 4 2 o

Another way to write x<4 and x≥2 2 ≤ x < 4 4 > x ≥ 2 Numbers that are greater than or equal to 2 and less than 4. ● 3 4 2 o

● ● 2) Graph x < 2 or x ≥ 4 a) Graph x < 2 o o b) Graph x ≥ 4 3 4 2 o 3 4 2 o b) Graph x ≥ 4 3 4 2 ● 3 4 2 ● c) Combine the graphs

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

4) Graph the compound inequality 6 < m < 8 When written this way, it is the same thing as 6 < m AND m < 8 Numbers that are greater than 6 and less than 8. 7 8 6 o

5) Which is equivalent to x > -5 and x ≤ 1? Answer Now

Translate the verbal phrase into an inequality Translate the verbal phrase into an inequality. Then graph the inequality. All real numbers that are greater than -2 and less than 3 All real numbers that are less than 0 or greater than or equal to 4

Remember, when written like this, it is an AND problem! 6) Graph 3 < 2m – 1 < 9 Remember, when written like this, it is an AND problem! 3 < 2m – 1 < 9 +1 +1 +1 4 < 2m < 10 2 2 2 2 < m < 5 5 -

● ● 7) 2x < -6 and 3x ≥ 12 o o o o Solve each inequality for x Graph each inequality Combine the graphs Where do they intersect? They do not! x cannot be greater than or equal to 4 and less than -3 No Solution!! -3 -6 o -3 -6 o 4 7 1 o ● 4 7 1 o ●

8) Graph x < 2 or x ≥ 4 5 -

The whole line is shaded!! 9) Graph x ≥ -1 or x ≤ 3 The whole line is shaded!!