Learn to solve inequalities with integers.

Inequalities & Integers

The graph of an inequality shows all of the numbers that satisfy the inequality. When graphing inequalities on a number line, use solid circles ( ) for and and open circles ( ) for > and <.

Remember!

k > –5

A. k +3 > –2

Subtract 3 from both sides.–3 –3

k +3 > –2

Solve and graph.

–5 0

B. r – 9 12

r 21

Add 9 to both sides.r – 9 + 9 12 + 9r – 9 12

21 2415

Solve and graph.

–5 1

5 is greater than –1.

Sometimes you must multiply or divide to isolate the variable. Multiplying or dividing both sides of an inequality by a negative number gives a surprising result.

5 > –1 Multiply both sides by –1.–1 • 5 –1 • (–1) > or < ?

You know –5 is less than 1, so you should use <.

–5 < 1

–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7

–5 < 1

5 > –1

3 > 1

–4 12

Multiply by –2

Divide by –4 1 –3

–6 < –2

MULTIPLYING INEQUALITIES BY NEGATIVE INTEGERS

Words Original Inequality

Multiply/Divide

Result

Multiplying or dividing by a negative number reverses the inequality symbol.

The direction of the inequality changes only if the number you are using to multiply or divide by is negative.

Helpful Hint

A. –3y 15

y –5

Divide each side by –3; changes to .

B. 7m < 21

m < 3

Divide each side by 7.

Solve and graph.

0 3–3 5

–3y 15–3 –3

7m < 21 7 7

–7 –5 0 4

Solve and graph.1. h + 2 < 0

2. c – 5 > –2

7n > 28

t

–33. < 1

h –2

n > 4

t > –3

c 3

–2 0 2

3–3 0

3–3 0

4 8 04.

Solve and graph.1. -3 – 2n > 1

2. -4 – 2r < –6

+ 5 < 6

x

53. – 1 > 1

n –2

r < 6

x 10

r > 1

–2 0 2

0

100

6 9 04. r

6

Two-step Inequalities.

Solve and graph.1. -1 + 2m > 15

2. -5k + 1 > 21

+ 1 > 0

t

43. + 5 > 4

n 8

x -8

t -4

k < -4

0 8

0

-4 0

0 -84. x

8

-4

Two-step Inequalities.