Ch 2.1 (part 2)One Step Inequalities (Multiplication)

Objective:

To solve and graph simple inequalities involving multiplication and division.

Definitions• Multiplication Property of Inequality:

When multiplying by a negative number, the inequality symbol reverses.

In other words, “FLIP” the inequality sign

• Division Property of Inequality:

When dividing by a negative number, the inequality symbol reverses.

In other words, “FLIP” the inequality sign

flip

Inequalities transform like equations except...

When multiplying or dividing by a negativenumber you must reverse (flip) the inequality.

-4 -3 -2 -1 0 1 2 3 4

Positive sideNegative side

Large is largeLarge is small

Rules

-3 < -2 3 > 23 > 2(-1) (-1)

-3 -2<

Why?Example using Multiplication/Division:

-x < 1-1 -1

x > -1 (The inequality “flipped”)

Same example using Addition/Subtraction:

- x < 1

+ x + x

0 < 1 + x

- 1 < -1

-1 < x = x > -1

Example 1

Example 3

Example 2

Example 4

4 4

0 5 -6 0

-6 0 -21 0

x 5≤

(3) (3)

x -6>

(-3) (-3)

y -21≤x -6>

€

4x ≤ 20

€

x

3> −2

€

−4 x < 24

€

−4 −4

€

y

−3≥ 7

Example 5 Example 6

Example 7 Example 8

-6 0

3 3

-12 0

-2 0

(-2) (-2)

<x -6

x -2≥

m -12>

€

−13

8<

n

8(8) (8)

-13 n< n > -13

-13 0

€

3x < −18

€

m

−2< 6

€

−3x ≤ 6

€

−3 −3

1) 2)

Graph the following inequalities.

3) 4)

Classwork

0 0

0 0

€

−7 >b

6

€

−2 < −r

7

€

60 ≤ −3x

€

−18 ≤ 6v

5) 6)

7) 8)

0 0

0 0

€

n

6≤ −5

€

−b

6≤

5

3

€

n

3< −5 -2k < 8