TODAY YOU WILL LEARN HOW TO SOLVE INEQUALITIES USING MULTIPLICATION AND DIVISION

Solving Inequalities Using Multiplication & Division

SOLVING INEQUALITIES USING MULTIPLICATION

x -2 3

x -2 3 x -6

Translation: x divided by 3 is greater than or equal

to negative 2.

The opposite of divided by 3 is Multiplying by 3.

What you do on one side you do on the other!

3 • • 3

Graph

-2 0 4-4-6

SOLVING INEQUALITIES USING DIVISION

3x ≤ 12

3x ≤ 12 3

Translation: 3 times x is less than or equal to 12.

The opposite of multiplying by 3 is divided by 3.

What you do on one side you do on the other!31

Graph

0 2 4-2-4

x ≤ 4

SOLVE THE INEQUALITY. THEN GRAPH THE SOLUTION.

k210)2 3

6)1r

MULTIPLYING AND DIVIDING INEQUALITIES BY A NEGATIVE NUMBER Solve the inequality.

12 > -3m

-4 < m

Step1: solve for m -divide by -3

Step 2: reverse the inequality symbol-3 -3

<12 > -3m

When multiplying or dividing by a negative number on both sides reverse the inequality symbol.

Solve the inequality. k < -3

Step1: solve for k -Multiply by -2

Step 2: reverse the inequality symbol>

-2.

When multiplying or dividing by a negative number on both sides reverse the inequality symbol.

-2

.-2

k > 6

MULTIPLYING AND DIVIDING INEQUALITIES BY A NEGATIVE NUMBER

TELL WHETHER THE OPERATION REVERSES THE SIGN OF THE INEQUALITY.

1) Multiply each side by -1

2) Multiply each side b

3) Divide each side by 4.

4) Divide each side by -5.

1

4

YOU TRY: SOLVE AND GRAPH THE INEQUALITIES

162)1 x

4)7 m4

2)x

510

3) 4k 12

EXIT TICKET

Solve and graph the inequality: 8x < –24

Additional Example: Application

$4.30 times number of tubes is at most $20.00.

4.30 • p ≤ 20.00

Jill has a $20 gift card to an art supply store where 4 oz tubes of paint are $4.30 each after tax. What are the possible numbers of tubes that Jill can buy?

Let p represent the number of tubes of paint that Jill can buy.

4.30p ≤ 20.00

p ≤ 4.65…

Since p is multiplied by 4.30, divide both sides by 4.30. The symbol does not change.

Since Jill can buy only whole numbers of tubes, she can buy 0, 1, 2, 3, or 4 tubes of paint.

Additional Example ContinuedJill has a $20 gift card to an art supply store where 4 oz tubes of paint are $4.30 each after tax. What are the possible numbers of tubes that Jill can buy?

Lesson QuizSolve each inequality and graph the solutions.

1. 8x < –24 x < –3 2. –5x ≥ 30 x ≤ –6

3. x > 20 4. x ≥ 6

5. A soccer coach plans to order more shirts for her team. Each shirt costs $9.85. She has $77 left in her uniform budget. What are the possible numbers of shirts she can buy?0, 1, 2, 3, 4, 5, 6, or 7 shirts