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.
Starting with $\displaystyle \frac{3}{2x}>\frac{3}{4}$
Multiply by 2/3 $\displaystyle \frac{2}{3}\cdot\frac{3}{2x}>\frac{2}{3}\cdot\frac {3}{4}$
This gives $\displaystyle \frac{1}{x}>\frac{1}{2}$
Then a little known rule says that if $\displaystyle \frac{a}{b}>\frac{c}{d}$ then $\displaystyle \frac{b}{a}<\frac{d}{c}$
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.)