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
Â· [x] < 

≤ 5
Â· [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.
