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:
![](./articles_imgs/1158/solvin2.GIF) |
![](./articles_imgs/1158/solvin3.GIF) |
Original inequality |
![](./articles_imgs/1158/solvin4.GIF) |
![](./articles_imgs/1158/solvin5.GIF) |
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:
![](./articles_imgs/1158/solvin6.GIF)
|