Warm UpSolve each equation. 1. –5a = 30 2.

Graph each inequality.

5. x ≥ –10

6. x < –3

–6 –10

3. 4.

Lesson 3.3Solving Inequalities by Multiplying or Dividing

≥

<

>

≤Less than or equal to

greater than greater than or equal to

Less than

Preparation for 5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.

California Standards

Inequalities and their Graphs

Terms you see and need to know to graph inequalities correctly

Notice colored in circles

≤ is less than or equal to

≥ is greater than or equal to

Inequalities and their Graphs

Terms you see and need to know to graph inequalities correctly

Notice

open circles

< is less than

> is greater than

Solving Inequalities Using MultiplicationSolving 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 DivisionSolving Inequalities Using Division

3x ≤ 12

3x ≤ 12 3

Translation: 3times 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 Solve the inequality. Then graph the solution.graph the solution.

k210)2 3

6)1r

Multiplying and Dividing Inequalities by aMultiplying and Dividing Inequalities by a

Negative NumberNegative 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 reverse the inequality symbol.

Multiplying and Dividing Inequalities by a Negative Number

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 reverse the inequality symbol.

-2

.-2

k > 6

Tell whether the operation reverses Tell whether the operation reverses

the sign of the inequality.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 the InequalitiesYou try: Solve the Inequalities

1) 2x 16

4)7 m4

2)x

510

3) 4k 12

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