Solving Linear Inequalities with Fractions
Example
An inequality with fractions
Solve
State and graph the solution set.
Solution
First multiply each side of the inequality by 6, the LCD:


Original inequality 


Multiplying by positive 6 does not reverse the inequality 
3x  4 
≤ 6x + 8 
Distributive property 
3x 
≤ 6x + 12 
Add 4 to each side 
3x 
≤ 12 
Subtract 6x from each side 
x 
≤ 4 
Divide each side by 3 and reverse the inequality 
The solution set is the interval [4, ∞). Its
graph is shown below:
