Solving Two-Step Inequalities
Remember!
Draw a closed circle when the inequality includes
the point and an open circle when it does not
include the point.
When you solve two-step equations,
you can use the order of operations in
reverse to isolate the variable. You can
use the same process when solving
two-step inequalities.
Additional Example 1A: Solving Two-Step
Inequalities
Solve. Then graph the solution set on a
number line.
A. y – 6 > 1
2
y
2 –6>1
+6 +6
Add 6 to both sides.
y
>7
2
y
Multiply both sides by 2.
(2) 2 > (2)7
y > 14
– 21
– 14
–7
0
7
14
21
1
Additional Example 1B: Solving Two-Step
Inequalities
Solve. Then graph the solution set on a
number line.
B. m + 8 ≤ 5
–3
m +8≤5
–3
– 8 –8
Subtract 8 from both sides.
m
≤ –3
–3
(–3) m ≥ (–3)(–3) Multiply both sides by –3, and
–3
reverse the inequality symbol.
m≥9
•
–3
0
3
6
9
12
15
Additional Example 1D: Solving Two-Step
Inequalities
Solve. Then graph the solution set on a
number line.
D. –3x + 5 ≤ –4
–3x + 5 ≤ –4
– 5 –5
–3x
≤ –9
–3x ≥ –9
–3
–3
x ≥ 3
–9 –6 –3
0
3 6
Subtract 5 from both sides.
Divide both sides by –3, and
reverse the inequality
symbol.
9
Additional Example 1C: Solving Two-Step
Inequalities
Solve. Then graph the solution on a number
line.
C. 4y – 5 < 11
4y – 5 < 11
+5 +5
4y
< 16
4y
< 16
4
4
y<4
–6
–4 –2
0
Add 5 to both sides.
Divide both sides by 4.
º
2 4
6
Try This: Example 1A
Solve. Then graph the solution set on a
number line.
A. h + 1 > –1
7
h
7 + 1 > –1
–1
–1
Subtract 1 from both sides.
h
> –2
7
h
(7) 7 > (7)(–2) Multiply both sides by 7.
h > –14
– 21
– 14
–7
0
7
14
21
2
Try This: Example 1B
Solve. Then graph the solution set on a
number line.
B. m + 1 ≥ 7
–2
m +1≥7
–2
– 1 –1
Subtract 1 from both sides.
m
≥ 6
–2
(–2) m ≤ (–2)(6) Multiply both sides by –2, and
–2
reverse the inequality symbol.
m ≤ –12
Try This: Example 1C
Solve. Then graph the solution on a number
line.
C. 2y – 4 > –12
2y – 4 > –12
+4 +4
2y
> –8
2y
> –8
2
2
y > –4
º
•
–18 –12 –6
0
6
12
18
–6 –4 –2
0
2 4
Add 4 to both sides.
Divide both sides by 2.
6
Try This: Example 1D
Solve. Then graph the solution set on a
number line.
D. –9x + 4 ≤ 31
–9x + 4 ≤ 31
– 4 –4
–9x
≤ 27
–9x ≥ 27
–9
–9
x ≥ –3
–9 –6 –3
0
3 6
Subtract 4 from both sides.
Divide both sides by –9,
and reverse the inequality
symbol.
9
3
4