# Thread: Solving fractions for X

1. ## Solving fractions for X

Starting to learn latex and also need to some help: I am trying to solve the equation below:

$\displaystyle \frac{x}{7} - \frac{1}{2} = 1 - \frac{2x}{5}$

The only thing I can think to do is start multiplying out the $\displaystyle \frac{1}{2}$:

$\displaystyle 2\frac{x}{7} - = 2 x 1 - 2\frac{2x}{5}$

or to find a common denominator on the left:

$\displaystyle \frac{2x -7}{14} = 1 - \frac{2x}{5}$

Either way after these I am getting lost if anyone could point out the right direction to me would be great.

Thanks

2. The first step is to perform the subtractions on each side by getting a common denominator.

3. $\displaystyle \frac{x}{7} - \frac{1}{2} = 1 - \frac{2x}{5}$
You could multiply everything by the LCD (which will be 7*2*5 = 70).
Then you'll have 10x - 35 = 70 - 28x.
Can you take it from here?

4. Ok so tell me if I got this right:

$\displaystyle 10x - 35 = 70 - 28x$

Then I

$\displaystyle 10x + 28x - 35 = 70$

$\displaystyle 38x - 35 = 70$

$\displaystyle 38x = 70 + 35$

$\displaystyle x = \frac {70 + 35}{38}$

$\displaystyle x = 2\frac {29}{38}$

Sorry for all the question hopefully im close to the answer now

5. I'd just leave it as x = 105/38, but that's just me...