1. Solve an inequality using subtraction
EXAMPLE 4
Solve an inequality using subtraction
Solve 9 x + 7. Graph your solution.
>
9 ≥ x + 7
Write original inequality.
9 – 7 ≥ x + 7 – 7
Subtract 7 from each side.
2 ≥ x
Simplify.
ANSWER
You can rewrite 2 ≥ x as x ≥ 2. The solutions are all real numbers less than or equal to 2.

2. 7. Solve y + 5.5 > 6. Graph your solution.
GUIDED PRACTICE
for Examples 4 and 5
7. Solve y > 6. Graph your solution.
SOLUTION
y > 6
Write original inequality.
y –5.5 > 6 –5.5
Subtract 5.5 from each side.
y > 0.5
Simplify.
ANSWER
You can rewrite 0.5 < y as y > The solutions are all real numbers greater than or equal to 0.5 .

3. Solve an inequality using addition
EXAMPLE 3
Solve an inequality using addition
x – 5 > – 3.5. Graph your solution.
Solve
x – 5 > – 3.5
Write original inequality.
x – > –
Add 5 to each side.
x > 1.5
Simplify.
ANSWER
The solutions are all real numbers greater than 1.5. Check by substituting a number greater than 1.5 for x in the original inequality.

4. Solve the inequality. Graph your solution.
GUIDED PRACTICE
for Example 3
Solve the inequality. Graph your solution.
4. x – 9 ≤ 3
SOLUTION
x – 9 ≤ 3
Write original inequality.
x – ≤ 3 + 9
Add 9 to each side.
x ≤ 12
Simplify.
ANSWER
The solutions are all real numbers less than 12. Check by substituting a number less than 12 for x in the original inequality.

5. GUIDED PRACTICE for Example 3 5. p – 9.2 < – 5 SOLUTION
Write original inequality.
p – < –
Add 9.2 to each side.
x < 4.2
Simplify.
ANSWER
The solutions are all real numbers less than 4.2. Check by substituting a number less than 4.2 for x in the original inequality.

6. The solutions are all real numbers less than
GUIDED PRACTICE
for Example 3
6. – 1 ≥ m – 1 2
– 1 ≥ m – 1 2
Write original inequality.
– ≥ m + 1 2
Add to each side. 1 2
≥ m 1 2 –
Simplify.
ANSWER
The solutions are all real numbers less than
. Check by substituting a number less
than for x in the original inequality. 1 2 –