Warm-up #12 ab 1 3x  1814x  x > 32-5x < x  -3 7x > x < x  -24

4.4 Using the Properties Together Goal: Solve inequalities using the addition and multiplication properties

Steps to solve inequalities 1. Distribute 2. Combine Like Terms 3. Get the variables on one side and constants on the other by (API) 4. Solve for the variable by using (MPI)

2-Step Inequalities 6 + 5y > y > y > 15 y > 3

Solve the inequality and graph the solutions. Check your answer. x < –11 –5 x + 5 < –6 –20 –12–8–4 –16 0 –11 Since x + 5 is divided by –2, multiply both sides by –2 to undo the division. Change > to <. Since 5 is added to x, subtract 5 from both sides to undo the addition. The solution set is { x:x < –11 }.

Solve the inequality and graph the solutions. Check your answer. Check Check the endpoint, – 11 3 Check a number less than – > 3

Solve the inequality and graph the solutions. 2 – (–10) > –4t 12 > –4t –3 < t (or t > –3) Combine like terms. Since t is multiplied by –4, divide both sides by –4 to undo the multiplication. Change > to <. –3 –10 –8 –6–4 – The solution set is { t:t > –3 }.

Solve the inequality and graph the solutions. –4(2 – x) ≤ 8 −4(2 – x) ≤ 8 −4(2) − 4(−x) ≤ 8 –8 + 4x ≤ x ≤ 16 x ≤ 4 Distribute –4 on the left side. Since –8 is added to 4x, add 8 to both sides. Since x is multiplied by 4, divide both sides by 4 to undo the multiplication. –10 –8 –6–4 – The solution set is { x:x ≤ 4 }.

Solve the inequality and graph the solutions. 4f + 3 > 2 –3 4f > –1 Multiply both sides by 6, the LCD of the fractions. Distribute 6 on the left side. Since 3 is added to 4f, subtract 3 from both sides to undo the addition.

4f > –1 Since f is multiplied by 4, divide both sides by 4 to undo the multiplication. 0 The solution set is { f: f > }. Solve the inequality and graph the solutions.

-6x + 7 – x + 1 < 2x x + 8 < 2x x 8 < 9x < 9x

5(12-3t) ≥15(t+4) t ≥ 15t t ≥ 0 t ≤ 0

Assignment Page 184 (12-48) even