(x+4)/2 = (x-3)/3
I know you need to multiply both sides by the Least common multiple for the denominator, but then I get lost. please help me.
Okay, but then what would I do for this one when I need to find the least common multiple?
2/3x + 1/2 = 5/6x
I know the LCM is 6, but not sure what goes on after that. I have been doing math all day and really just drawing blanks now. Please explain to me the steps.
Before I get going: Saranya is right, dubulus made an error when he divided by 2x (just clearing that up for agentlopez)
$\displaystyle \frac{2}{3}x+\frac{1}{2}=\frac{5}{6}x$
The first thing I like to do is bring all the x's to the same side:
$\displaystyle \frac{1}{2} = \frac{5}{6}x-\frac{2}{3}x$
Then you bring it all together:
$\displaystyle \frac{1}{2} = \left( \frac{5}{6}-\frac{2}{3}\right) x$
Now you need to subtract those two fractions from each other, so you need to find the least common multiple.
$\displaystyle \frac{1}{2} = \left( \frac{5}{6}-\frac{4}{6}\right) x$
Then you can put it all together:
$\displaystyle \frac{1}{2} = \frac{5-4}{6}x \quad\rightarrow\quad \frac{1}{2} = \frac{1}{6}x$
Then to solve for x, you have to divide away that 1/6:
$\displaystyle \frac{1}{2} \div \frac{1}{6}=x$
So now we cross multiply:
$\displaystyle \frac{1}{2} \nearrow\!\!\!\!\!\!\searrow\!\!\!\!\!\!\nwarrow \!\!\!\!\!\!\swarrow \frac{1}{6}=x$
and we get:
$\displaystyle \frac{6}{2}=x\quad\rightarrow\quad\boxed{x=3}$
Just in case agentlopez is trying to figure out why people are giving different answers to the second problem, Quick clearly and correctly got x=3 out of
and Saranya, also correctly, got x = 1/3 out of
$\displaystyle \frac{2}{3x}+\frac{1}{2} = \frac{5}{6x}$
You should make sure you understand the post that solved the problem you were trying to ask.