Solving Rational Inequalities

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October 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?

Thanks in advance.
October 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 ?
October 23rd 2011, 12:44 PM
Dragon08

Re: Solving Rational Inequalities

3/2x>3/4. Then, I divided both sides by 3/2.
October 23rd 2011, 12:54 PM
SammyS

Re: Solving Rational Inequalities

That gives (1/x) > (1/2) .
October 23rd 2011, 12:55 PM
Dragon08

Re: Solving Rational Inequalities

How did you get that?
October 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 ?
October 23rd 2011, 02:07 PM
Dragon08

Re: Solving Rational Inequalities

Yes
October 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 $\frac{b}{a}<\frac{d}{c}$
October 23rd 2011, 02:53 PM
Dragon08

Re: Solving Rational Inequalities

Okay, I get it. Thank you
November 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?

Thanks in advance.

A large part of your problem is that what you give as the question itself is ambiguous- use parentheses!

If the problem was (5/6)x+(2/3)x>3/4, then x> 1/2 is exactly right. However, it appears that your problem is really 5/(6x)+ 2/(3x)> 3/4. If that is what the inequality is, then, as SammyS said, you arrive at 1/x> 1/2 so that 0< x< 2. (If 1/x> 1/2 then x must be positive.)