5-4 Compound Inequalities Goal: Solve and graph compound inequalities. Eligible Content: A1.1.3.1.1 / A1.1.3.1.2 / A1.1.3.1.3

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.

x is a number greater than 1 or less than -2. 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!

x is a number greater than 2 and less than 5. 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 3 < x ≤ 5 x > 5 OR x ≤ -2 -4 ≤ x ≤ -1 x ≥ 3 OR x < 1

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

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

Solve –2x + 5 > 15 or 5x + 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 ≤ 3x – 8 ≤ 10 +8 + 8 + 8 6 ≤ 3x ≤ 18 3 3 3 2 ≤ x ≤ 6

Examples -5 ≤ 2x + 3 < 7 -2 < -2 – x < 1 -3 < -1 – 2x ≤ 5

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 3x + 7 < 13 AND 5x + 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”