Solving Two Step Equations

Two Step Inequalities

• You will solve these just like two step equations.

• Be careful when you are dividing or multiplying by a negative number– Remember you have to change the inequality

sign to its opposite.

Example 1

4x + 4 > -12

-4 -4

4x > -16

4 4

x > -4

-6 -5 -4 -3 -2

Check: x = -3

4x + 4 > -12

4(-3) + 4 > -12

-12 + 4 > -12

-8 > -12

Example 2

15 ≥ -2x + 5

-5 -5

10 ≥ -2x

-2 -2

-5 ≤ x

x ≥ -5

You have to switch the sign because you are dividing by a negative number!!

-7 -6 -5 -4 -3

Check: x = 0

15 ≥ -2x + 5

15 ≥ -2(0) + 5

15 ≥ 0 + 5

15 ≥ 5

Example 3

3(4x – 5) ≤ 9

12x – 15 ≤ 9

+15 +15

12x ≤ 24

12 12

x ≤ 2

0 1 2 3 4

Check: x = 0

3(4x – 5) ≤ 9

3(4(0) – 5) ≤ 9

3(0 – 5) ≤ 9

3(-5) ≤ 9

-15 ≤ 9

Example 4

3(-2x + 8) < 54

-6x + 24 < 54

-24 -24

-6x < 30

-6 -6

x > -5

You have to switch the sign because you are dividing by a negative number!!

-7 -6 -5 -4 -3

Check: x = 0

3(-2x +8) < 54

3(-2(0) +8) < 54

3(0 + 8) < 4

3(8) < 54

24 < 54