# Solving Rational Inequalities

• Oct 23rd 2011, 12:38 PM
Dragon08
Solving Rational Inequalities
Solve this inequality: 5/6x+2/3x>3/4.
So I simplified the left side and got 3/2x, then moved the equation to one side and got 3/2x-3/4>0. I got x>1/2, but the answer is wrong.
Can somebody help me?

• Oct 23rd 2011, 12:42 PM
SammyS
Re: Solving Rational Inequalities
Lets see your work. How did you get x>1/2 , from 3/2x-3/4>0 ?
• Oct 23rd 2011, 12:44 PM
Dragon08
Re: Solving Rational Inequalities
3/2x>3/4. Then, I divided both sides by 3/2.
• Oct 23rd 2011, 12:54 PM
SammyS
Re: Solving Rational Inequalities
That gives (1/x) > (1/2) .
• Oct 23rd 2011, 12:55 PM
Dragon08
Re: Solving Rational Inequalities
How did you get that?
• Oct 23rd 2011, 01:06 PM
SammyS
Re: Solving Rational Inequalities
Using algebra ... and assuming what you meant was 3/(2x) > 3/4 .

Was the original problem: Solve 5/(6x) + 2/(3x) > 3/4 ?
• Oct 23rd 2011, 02:07 PM
Dragon08
Re: Solving Rational Inequalities
Yes
• Oct 23rd 2011, 02:33 PM
SammyS
Re: Solving Rational Inequalities
Quote:

Originally Posted by SammyS
Using algebra ... and assuming what you meant was 3/(2x) > 3/4 .

Was the original problem: Solve 5/(6x) + 2/(3x) > 3/4 ?

Quote:

Originally Posted by Dragon08
Yes

Starting with     $\frac{3}{2x}>\frac{3}{4}$

Multiply by 2/3    $\frac{2}{3}\cdot\frac{3}{2x}>\frac{2}{3}\cdot\frac {3}{4}$

This gives       $\frac{1}{x}>\frac{1}{2}$

Then a little known rule says that if   $\frac{a}{b}>\frac{c}{d}$ then   $\frac{b}{a}<\frac{d}{c}$
• Oct 23rd 2011, 02:53 PM
Dragon08
Re: Solving Rational Inequalities
Okay, I get it. Thank you
• Nov 4th 2011, 06:21 AM
HallsofIvy
Re: Solving Rational Inequalities
Quote:

Originally Posted by Dragon08
Solve this inequality: 5/6x+2/3x>3/4.
So I simplified the left side and got 3/2x, then moved the equation to one side and got 3/2x-3/4>0. I got x>1/2, but the answer is wrong.
Can somebody help me?