Solving MultiStep Inequalities Lesson 4 4 Algebra 1

Solving Multi-Step Inequalities Lesson 4 -4 Algebra 1 Additional Examples Solve 5 + 4 b < 21. 5 + 4 b – 5 < 21 – 5 4 b < 16 Simplify. 4 b 16 < 4 4 Divide each side by 4. b<4 Check: Subtract 5 from each side. 5 + 4 b = 21 5 + 4(4) 21 Simplify. Check the computation. Substitute 4 for b. 21 = 21 5 + 4 b < 21 5 + 4(3) < 21 17 < 21 Check the direction of the inequality. Substitute 3 for b.

Solving Multi-Step Inequalities Lesson 4 -4 Algebra 1 Additional Examples 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? Relate: twice the length Write: 2(20) plus twice the width can be no more than + 2 w < the length of trim 48

Solving Multi-Step Inequalities Lesson 4 -4 Algebra 1 Additional Examples (continued) 2(20) + 2 w < 48 40 + 2 w – 40 < 48 – 40 Simplify 2(20). Subtract 40 from each side. 2 w < 8 Simplify. 2 w < 8 2 2 Divide each side by 2. w< 4 Simplify. The banner’s width must be 4 feet or less.

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

Solving Multi-Step Inequalities Lesson 4 -4 Algebra 1 Additional Examples 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. 5 z 18 < 5 5 Divide each side by 5. 3 z < 35 Simplify.

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