Section 3-3 Solve Inequalities using Multiplication & Division

SPI 22N: identify the graphical representation of the solution to a one variable inequality

Objectives:• Use multiplication and division to solve inequalities

Consider the inequality 4 > 1.

1. Complete each statement at the right with the appropriate inequality sign.

4 ∙ 3 1 ∙ 3

4 ∙ 2 1 ∙ 2

4 ∙ 1 1 ∙ 1

4 ∙ 0 1 ∙ 0

4 ∙ -1 1 ∙ -1

4 ∙ -2 1 ∙ -2

4 ∙ -3 1 ∙ -3

>

>

>

=

<

<

<

2. What happens to the symbol when you multiply each side by a positive number?

3. What happens to the symbol when you multiply each side by 0?

4. What happens to the symbol when you multiply each side by a negative number?

Multiplication Property of Inequality: For every real number a and b, and for c < 0

Properties of Inequalities

if a > b then ac < bc . . . and . . . if a < b, then ac > bc

If a = 4, b = 2 and c = -2 . . . Then . . . 4 > 2 and 4(-2) < 2(-2)

If c > 0, solve like an equality.

Division Property of Inequality: For every real number a and b, and for c < 0

Properties of Inequalities

if a > b then a < b . . . and . . . c c if a < b, then a > b c c

If a = 4, b = 2 and c = -2 . . . Then . . . 4 > 2 and 4 < 2 -2 -2

If c > 0, solve like an equality.

Solve the inequality

Solve using the Properties of Inequalities

244 c

4

24

4

4

c Since you have to divide by a negative

number, change the inequality sign

6 c Simplify

Solve the inequality

Solve using the Properties of Inequalities

03

4y

Multiply each side by the reciprocal of the coefficient of y. Do not change the sign, because you are not multiplying by a negative value.

0y Simplify

4

30

3

4

4

3y

Your family budgets $160 to spend on fuel for a trip. How many times can they fill the car’s gas tank if it cost $25 each time?

Solve using the Properties of Inequalities

Define a variable for the unknown:x = number of times car can be filled

25x ≤ 160

Write an Inequality:

25x ≤ 16025 25

Solve the Inequality

x ≤ 6.4

Answer the question: The car can be filled at least 6 times.