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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:

 
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