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 _________ Then, cross out zero pairs (1 red and 1 yellow square is a zero pair).

4. ALGEBRA READINESS Example: Solve 2y – 3  -5. 2y - 3 < -5Given. 2y < -2 Simplify. y < -1 Simplify. Check: 2y - 3 < -5 2y - 3 < -5Check to make sure -1 makes both sides equal. 2(-2) - 3 < -5Substitute a solution less than – 1 for b like -2. 2(-1) - 3 -5Substitute -1 for y. -5 = -5 -7 < -5 Check that the direction of the sign is correct. Division Property of Equality. 2 2 “Solving Two-Step Inequalities” (9-5) + 0 +3 +3 Addition Property of Equality. _________

5. ALGEBRA READINESS a. ) Example: Solve -9 – x + 6.  1313 -9 – x + 6  1313 - 6 - 6 Subtraction Property of Equality. 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. 1313 -9 = -9 -9  – (60) + 6 1313 -9  -14 “Solving Two-Step Inequalities” (9-5) + 0 ____________ Check to make sure the solution makes both sides of the equation equal. Check the direction of the inequality by substituting x for a value bigger than 45, like 60.

6. ALGEBRA READINESS b.) Solve – 5x – 2 > – 12. – 5x – 2 > 12 – 5x – 10 Simplify. Addition Property of Inequality. + 2 + 2 x < 2 Simplify. – 5 – 5 Division Property of Inequality. Reverse the Direction of the inequality sign. Solving Two-Step Inequalities LESSON 9-5 Additional Examples 1 1 + 0 ____________ > < Check: Step 1 Check to make sure 2 makes both sides of the equation equal.. – 5x – 2 = – 12 Write the related equation. – 5(2) – 2 = – 12 Substitute 2 for x. – 10 – 2 = – 12 Use the order of operations. – 12 = – 12 Step 2 Check the direction of the inequality symbol – 5x – 2 > – 12 – 5(0) – 2 > – 12 Substitute a number less than 2 for x. –2 > – 12

7. 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 Solving Two-Step Inequalities LESSON 9-5 Additional Examples ____________ 7b ≤ 21 Simplify. 0 + 7 7 Use the Division Property of Inequality. b ≤ 3 Simplify. You can buy 3 books.

8. 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