Multi-Step Inequalities 3-4 Solving Two-Step and Multi-Step Inequalities Holt Algebra 1 Warm Up Lesson Presentation Lesson Quiz- EXIT EXAM

Warm Up Solve each equation. 1. 2x – 5 = –17 2. –6 14 Solve each inequality and graph the solutions. 3. 5 < t + 9 t > –4 4. a ≤ –8

Objective Solve inequalities that contain more than one operation.

Solve the inequality and graph the solutions. A. –12 ≥ 3x + 6 –10 –8 –6 –4 –2 2 4 6 8 10

Solve the inequality and graph the solutions. B. –20 –12 –8 –4 –16 Clear the fraction first! (Undo the division)

Simplifying Before Solving Inequalities C. 3 + 2(x + 4) > 3 –10 –8 –6 –4 –2 2 4 6 8 10

D. Clear the fraction! Multiply both sides by 8, the LCD of the fractions. Distribute 8 on the right side. 5 < 3x – 2 Since 2 is subtracted from 3x, add 2 to both sides to undo the subtraction. +2 + 2 7 < 3x

Example D, Continued 7 < 3x Since x is multiplied by 3, divide both sides by 3 to undo the multiplication. 4 6 8 2 10

is greater than or equal to Application Problem: The average of Jim’s two test scores must be at least 90 to make an A in the class. Jim got a 95 on his first test. What grades can Jim get on his second test to make an A in the class? Let x represent the test score needed. The average score is the sum of each score divided by 2. First test score plus second test score divided by number of scores is greater than or equal to total score (95 + x)  2 ≥ 90

Application Continued Clear the fraction!! Since 95 + x is divided by 2, multiply both sides by 2 to undo the division. 95 + x ≥ 180 Since 95 is added to x, subtract 95 from both sides to undo the addition. –95 –95 x ≥ 85 The score on the second test must be 85 or higher.

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Lesson Quiz: Part I Solve each inequality and graph the solutions. 1. 13 – 2x ≥ 21 x ≤ –4 2.