A powerpoint presentation for first year Algebra. Lesson on solving multi-step inequalities that contains examples and applications.

1. Chapter 3 Solving Inequalities 3-4: Solving Multi-Step Inequalities Ren Foshee Algebra 1-2

2. Warm-Up

4. Solve 5 + 4 b < 21. 5 + 4 b – 5 < 21 – 5 Subtract 5 from each side. 4 b < 16 Simplify. b < 4 Simplify. Check: 5 + 4 b = 21 Check the computation. 5 + 4 b < 21 Check the direction of the inequality. 5 + 4( 3 ) < 21 Substitute 3 for b . Solving Multi-Step Inequalities LESSON 3-4 5 + 4( 4 ) 21 Substitute 4 for b . 21 = 21 17 < 21 < Divide each side by 4. 4 b 4 16 4

5. The band is making a rectangular banner that is 20 feet long with trim around the edges. What are the possible widths the banner can be if there is no more than 48 feet of trim? Solving Multi-Step Inequalities LESSON 3-4 twice the the length length of trim Relate: plus twice the width can be no more than Write: 2(20) + 2 w 48 <

6. (continued) The banner’s width must be 4 feet or less. Solving Multi-Step Inequalities LESSON 3-4 2(20) + 2 w 48 < 40 + 2 w 48 Simplify 2(20). < 40 + 2 w – 40 48 – 40 Subtract 40 from each side. < 2 w 8 Simplify. < w 4 Simplify. < Divide each side by 2. < 2 w 2 8 2

7. Solve 3 x + 4(6 – x ) < 2. 3 x + 24 – 4 x < 2 Use the Distributive Property. – x + 24 < 2 Combine like terms. – x + 24 – 24 < 2 – 24 Subtract 24 from each side. – x < –22 Simplify. x > 22 Simplify. Solving Multi-Step Inequalities LESSON 3-4 > Divide each side by –1. Reverse the inequality symbol. – x – 1 – 22 – 1

8. Solve 8 z – 6 < 3 z + 12. 8 z – 6 – 3 z < 3 z + 12 – 3 z Subtract 3 z from each side. 5 z – 6 < 12 Combine like terms. 5 z – 6 + 6 < 12 + 6 Add 6 to each side. 5 z < 18 Simplify. Solving Multi-Step Inequalities LESSON 3-4 < Divide each side by 5. 5 z 5 18 5 z < 3 Simplify. 3 5

9. Solve 5(–3 + d ) 3(3 d – 2). Solving Multi-Step Inequalities LESSON 3-4 < – 15 – 4 d + 15 –6 + 15 Add 15 to each side. < – 4 d 9 Simplify. < – 15 + 5 d – 9 d 9 d – 6 – 9 d Subtract 9 d from each side. < – 15 – 4 d –6 Combine like terms. < – 15 + 5 d 9 d – 6 Use the Distributive Property. < d –2 Simplify. > 1 4 Divide each side by –4. Reverse the inequality symbol. – 4 d – 4 9 – 4 >