Solving Compound Linear Inequalities
Example
Solve:
Then, graph the solution on a number line.
| Solution |
x < |
 |
≤ x + 3 |
| To clear the fractions, multiply
each part by the LCD, 5.
|
5
· [x] < |
 |
≤ 5
· [x
+ 3] |
| Distribute.
Subtract 4 from each part.
Simplify.
Subtract 5x from each part.
Simplify. |
5x <
5x - 4 <
5x - 4 <
5x - 4 - 5x <
-4 < |
7x + 4
7x + 4 - 4
7x
7x - 5x
2x |
≤ 5x + 15
≤ 5x + 15 - 4
≤ 5x + 11
≤ 5x + 11 - 5x
≤ 11 |
| Divide each part by 2. |
< |
 |
≤
 |
| Simplify. |
-2 < |
x |
≤
|
To graph the solution, place an open circle at -2 and a closed circle at
.
Then, shade the region between the plotted points.
