1. ALGEBRA READINESS LESSON 9-5 Warm Up Lesson 9-5 Warm-Up

2. ALGEBRA READINESS LESSON 9-5 Warm Up Lesson 9-5 Warm-Up

3. ALGEBRA READINESS “Solving Two-Step Inequalities” (9-5) (3-1) How do you solve a multi- step inequality? Tip: Solve a multi-step inequality exactly like an equality (equaltion with an equal sign). Isolate the variable (get the letter by itself) by: 1. “Undo”ing addition and subtraction from the variable side 2. “Undo”ing multiplication and division from the variable side Note: If the variables is on both sides, “undo” it from one side so that there is only one variable side before doing anything else 2 2 _ _ 1 1 + 3

4. ALGEBRA READINESS Example: Solve 2y – 3  -5. 2y - 3 + 3 < -5 + 3Add 3 to each side. 2y < -2 Simplify. y < -1Simplify. Check: 2y - 3 < -5 2y - 3 < -5Check the direction of the inequality. 2(-2) - 3 < -5Substitute a solution less than – 1 for b like -2. 2(-1) - 3 -5Substitute -1 for y. -5 = -5 -7 < -5 The direction of the sign is correct. < Divide each side by 2. 2y 2 -2 2 “Solving Two-Step Inequalities” (9-5) (3-1) + 0

5. ALGEBRA READINESS Example: Solve -9 – x + 6.  1313 -9 – x + 6  1313 -9 - 6 – x + 6 - 6  1313 Add 6 to each side. Simplify. -15 – x  1313 Simplify. 45  x or x  45 3131 –(-15) 3131 – 1313 –x To eliminate the coefficient - from the x side, divide both sides by - which is the same as multiplying each side by the reciprocal, - When you divide or multiply both sides by a negative, reverse the direction of the inequality symbol. 1313  1313 3131 Check: -9  – x + 6 1313 -9  – (45) + 6 Substitute 45 for x. 1313 -9 = -9 -9  – (60) + 6 Check the direction of the inequality by substituting x for a value bigger than 45, like 60. 1313 -9  -14 The direction of the sign is correct. “Solving Two-Step Inequalities” (9-5) + 0

6. ALGEBRA READINESS Solve – 5x – 2 > – 12. – 5x – 2 > – 12 – 5x > – 10 Simplify. Addition Property of Inequality. – 5x – 2 + 2 > – 12 + 2 x < 2 Simplify. – 5x – 5 – 10 – 5 < Isolate the variable. Use the Division Property of Inequality. Reverse the direction of the inequality sign. Solving Two-Step Inequalities LESSON 9-5 Additional Examples 1 1 0 +

7. ALGEBRA READINESS Step 1 Check whether your answer is a solution to the related equation. Check: – 5x – 2 = – 12 Write the related equation. Step 2 Check the inequality symbol by substituting into the inequality. (continued) – 5(2) – 2 = – 12 Substitute 2 for x. – 10 – 2 = – 12 Use the order of operations. – 5x – 2 > – 12 – 5(0) – 2 > – 12 Substitute a number less than 2 for x. – 12 = – 12 –2 > – 12 Solving Two-Step Inequalities LESSON 9-5 Additional Examples

8. ALGEBRA READINESS You have $50 to spend on books that cost $7 each and one bookcase that costs $29. How many books can you buy? Words cost of one plus cost of books is at most $50 bookcase Let b = the number of books. Equation 29 + 7b ≤ 50 29 + 7b ≤ 50 Subtraction Property of Inequality 29 – 29 + 7b ≤ 50 – 29 Solving Two-Step Inequalities LESSON 9-5 Additional Examples

9. ALGEBRA READINESS (continued) 7b ≤ 21 Simplify. b ≤ 3 Simplify. 7b77b7 21 7 ≤ Isolate the variable. Use the Division Property of Inequality. You can buy 3 books. Solving Two-Step Inequalities LESSON 9-5 Additional Examples 0 +

10. ALGEBRA READINESS Solve. 1.3x – 11 > 10 2. + 5 ≥ – 2 3.You want to order one large photo of yourself for $8.95 and some small photos for your friends. The small photos cost $.75 each. You have $25 to spend. Write an inequality you can use to find how many small photos you can order. Then solve it. r ≤ 28 x > 7 0.75p + 8.95 ≤ 25; p ≤ 21.4; 21 or fewer small photos r – 4 Solving Two-Step Inequalities LESSON 9-5 Lesson Quiz