Thread: 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.

Lets see your work. How did you get x>1/2 , from 3/2x-3/4>0 ?

3/2x>3/4. Then, I divided both sides by 3/2.

That gives (1/x) > (1/2) .

How did you get that?

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

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

Yes

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 ?

Originally Posted by Dragon08

Yes

Starting with    

Multiply by 2/3   

This gives      

Then a little known rule says that if    then    

Okay, I get it. Thank you

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.)