5 4 Compound Inequalities Goal Solve and graph

5 -4 Compound Inequalities Goal: • Solve and graph compound inequalities. Eligible Content: • A 1. 1. 3. 1. 1 / A 1. 1. 3. 1. 2 / A 1. 1. 3

Vocabulary • Compound Inequality – 2 inequality statements connected by AND or OR. • OR statements – x is either greater than one number or less than another number. • AND statements – x is between two numbers.

OR problems x is a number greater than 1 or less than -2. x > 1 OR x < -2

OR problems ▫ Always has the word OR in problem ▫ 2 separate inequalities pointing in opposite directions ▫ Graph is always 2 shaded areas pointing away from each other. You shade OUTSIDE the points!

AND problems x is a number greater than 2 and less than 5. x > 2 AND x < 5 2<x<5

AND problems ▫ Always has the word AND in written problem ▫ 1 inequality statement with 2 symbols pointing in the same direction (always< or ≤) ▫ Graph always has shading BETWEEN 2 points

Examples Graph each compound inequality 1. 3 < x ≤ 5 2. x > 5 OR x ≤ -2 3. -4 ≤ x ≤ -1 4. x ≥ 3 OR x < 1

Solving Compound Inequalities OR problems 2 x + 3 < 5 -3 -3 2 x < 2 2 2 x < 1 OR 4 x – 2 > 10 + 2 +2 4 x > 12 4 4 x > 3 x < 1 OR x > 3

Examples 1. 3 x+ 1 < 4 OR 2 x – 5 > 7 x < 1 OR x > 6 2. -6 x – 5 > 7 OR 8 x + 1 ≥ 25 x < -2 OR x ≥ 3

Solve – 2 x + 5 > 15 or 5 x + 15 > 20. A. x > -5 or x > 1 B. x < – 5 or x < 1 C. x < – 5 or x > 1 D. x < 1

Solving Compound Inequalities AND problems -2 ≤ 3 x – 8 ≤ 10 +8 +8 +8 6≤ 3 3 x 3 ≤ 18 3 2 ≤ x ≤ 6

Solve – 3 < x – 2 < 5. Then graph the solution. A. – 1 < x < 7 B. – 5 < x < 3 C. x < 7 D. – 1 < x < 3

Weird AND problems • 3 x + 7 < 13 AND 5 x + 2 > -13

REMEMBER WHEN YOU WRITE YOUR ANSWER: • OR problems – x should always be first • AND problems – x should be between 2 < symbols.

Practice Worksheet – “ 5 -4 Compound Inequalities”

Homework • Worksheet – “ 5 -4 Compound Inequalities Homework”