Solving Inequalities Using Multiplication or Division.Solving Multi- Step Inequalities.

What you’ll learn

To use multiplication or division to solve inequalities. To solve and graph simple inequalities and be able to justify each step.To solve multi-step inequalities. To represent and solve multi-step and real world applications that involves linear inequalities.

NoteThe same way you used to solve equations using multiplication and division you can use it now to solve inequalities.

You can use the multiplication and division property of inequality, just remember that when multiplying or dividing each side of an inequality by a negative number changes the meaning of the inequality. You need to reverse the inequality symbol to make the inequality true.

Example 1

Multiplying and dividing by a positive number

What are the solutions of? Graph the solutions

23

x

6

233

3

x

x

A.

Relate: money wanted

cost per dogs

timesnumber of

dogs is at least

4.50d ≥ 75

B. You walk dogs in your neighborhood after school. You earn $4.50 per dog. How many dogs you need to walk to earn at least $75.

Since d is the number of dogs and it has to be a positive integer, you must walk at least 17 dogs.

You solve it

Multiplying and dividing by a negative number

Example 2

What are the solutions of ? Graph the solutions

43r

7y 9

63y

9

9

3 x

21.52x

2

639y 1.52x

12r

433

r3

Your turn

1.2.

3.

4.

Answers:

1. x‹-62. w≤-33. a≤-44. c>14

Solving Multi-Step Inequalities

1. What are the solutions of? Check the solutions.9+4t > 21-9 -9 Subtract 9 from each side

4t > 12 Divide each side by 44 4t > 3

Check 9+4t > 21 9+4(3) > 21 25 > 21

Writing and Solving a Multi-Step Inequality

You want to fence in a rose bed that is adjacent to a deck. The length of your deck is 14 ft. You have at most 44 ft of fence. What are the possible widths of the rose bed?

14 ft

wlP 22 Because one side is the deck

w

w

w

wlP

15

230

21444

2

The width of the rose bed must be 15 ft or less.

Your turn

1.

2.

3.

4. In a community garden, you want to fence in a vegetable garden that is adjacent to your friend’s garden. You have 42 ft of fence. What are the possible lengths of you garden?

Answer: t>3

Answer: n >5

Answer: All real numbers

Answer: No solution

The length of the garden must be 9 ft or less

12 feet

Paul McCartneyhas been credited under the names of

Apollo C Vermouth and

Paul Ramon