5 4 Compound Inequalities Goal Solve and graph

















- Slides: 17

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”
Solving compound and absolute value inequalities
Compound inequalities worksheet
Quadratic inequality shading
Compound inequalities activity
Solving rational equations algebra 2
8-5 solving rational equations and inequalities
Solving inequalities using multiplication or division
Solving radical inequalities
Write equations and inequalities to solve problems.
Two step inequalities with fractions
Solve linear inequalities graphically
Solve inequalities
Graphing linear inequalities on a number line
Lesson 8 solve two step inequalities
Exponential and logarithmic inequalities
Two step inequalities
Solving rational equations and inequalities
Polynomial inequality definition