LESSON 3 4 SOLVING TWOSTEP AND MULTISTEP INEQUALITIES

LESSON 3. 4 SOLVING TWO-STEP AND MULTI-STEP INEQUALITIES

Solve inequalities that contain more than one operation

Inequalities that contain more than one operation require more than one step to solve. Use inverse operations to undo the operations in the inequality one at a time.

Step 1: Undo addition or subtraction Step 2: Undo multiplication and division Is your variable isolated?

Remember! Subtracting a number is the same as adding its opposite. 7 – 2 t = 7 + (– 2 t)

Solving Multi-Step Inequalities Solve the inequality and graph the solutions. 1. Add/ Subtract 45 + 2 b > 61 – 45 2 b > 16 2. Multiply/Divide The solution set is {b: b > 8}. b>8 0 2 4 6 8 10 12 14 16 18 20

Solving Multi-Step Inequalities Solve the inequality and graph the solutions. 8 – 3 y ≥ 29 – 8 1. Add/Subtract 2. Multiply/Divide – 3 y ≥ 21 y ≤ – 7 The solution set is {y: y – 7}. – 7 – 10 – 8 – 6 – 4 – 2 0 2 4 6 8 10

Solve and Graph the inequality

To solve more complicated inequalities, you may first need to simplify the expressions on one or both sides.

Simplifying Before Solving Inequalities Solve the inequality and graph the solutions. 2 – (– 10) > – 4 t 1. Combine like terms. 12 > – 4 t 2. Multiply/Divide – 3 < t (or t > – 3) The solution set is {t: t > – 3}. – 3 – 10 – 8 – 6 – 4 – 2 0 2 4 6 8 10

Simplifying Before Solving Inequalities Solve the inequality and graph the solutions. – 4(2 – x) ≤ 8 1. Distributive Property − 4(2 – x) ≤ 8 − 4(2) − 4(−x) ≤ 8 – 8 + 4 x ≤ 8 +8 +8 4 x ≤ 16 2. Add/Subtract 3. Multiply/Divide x≤ 4 – 10 – 8 – 6 – 4 – 2 The solution set is {x: x ≤ 4}. 0 2 4 6 8 10

Now you try… 1. 3 x – 7 > 2 x>3 4. x – 4 < 3 5 x < 35 2. 4 x + 1 -3 x ≥ -1 3. 2 x – 7 ≤ -3 x≤ 2 5. 15 + x ≥ 6 3 x ≥ -27

Lesson Quiz: Part I Solve each inequality and graph the solutions. 1. 13 – 2 x ≥ 21 x ≤ – 4 2. – 11 + 2 < 3 p p > – 3 3. 23 < – 2(3 – t) t>7 4.

Lesson Quiz: Part II 5. A video store has two movie rental plans. Plan A includes a $25 membership fee plus $1. 25 for each movie rental. Plan B costs $40 for unlimited movie rentals. For what number of movie rentals is plan B less than plan A? more than 12 movies