ALGEBRA READINESS

LESSON 9-5Warm Up Lesson 9-5 Warm-Up

ALGEBRA READINESS

LESSON 9-5Warm Up Lesson 9-5 Warm-Up

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 side2. “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 + 3 _________ Then, cross out zero pairs (1 red and 1 yellow square is a zero pair).

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Example: Solve 2y – 3 -5.2y - 3 < -5 Given.

2y < -2 Simplify.

y < -1 Simplify.

Check:  2y - 3 < -5

2y - 3 < -5 Check to make sure -1 makes both sides equal.2(-2) - 3 < -5 Substitute a solution less than – 1 for b like -2.

2(-1) - 3 -5 Substitute -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._________

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a. ) Example: Solve -9 – x + 6. 13

-9 – x + 6 13

- 6 - 6 Subtraction Property of Equality.

Simplify.-15 – x 13

Simplify. 45 x or x 45

31– (-15) 3

1– 13– 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.

13 1

331

Check: -9 = – x + 613

-9 = – (45) + 6.13

-9 = -9

-9 – (60) + 6 13

“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 substitutingx for a value bigger than 45, like 60.

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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 InequalitiesLESSON 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 = – 12Step 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

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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 InequalitiesLESSON 9-5

Additional Examples

____________7b ≤ 21 Simplify.0 +7

7 Use the Division Property of Inequality.

b ≤ 3 Simplify.

You can buy 3 books.

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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 InequalitiesLESSON 9-5

Lesson Quiz