# How do you solve \frac{3}{4} ( x + 2) - \frac{x}{5} \leq \frac{2}{5} ( 6- x ) + \frac{x}{4}?

Sep 24, 2016

$x = \frac{9}{7}$

#### Explanation:

We need to rearrange the equation to get $x \le$ something.

For the sake of rearranging, we can treat the $\le$ sign as an $=$ sign.

$\frac{3}{4} \left(x + 2\right) - \frac{x}{5} \le \frac{2}{5} \left(6 - x\right) + \frac{x}{4}$

First we multiply everything by $4$

$3 \left(x + 2\right) - \frac{4 x}{5} \le \frac{8}{5} \left(6 - x\right) + x$

Then we take $x$ from both sides

$3 \left(x + 2\right) - \frac{4 x}{5} - x \le \frac{8}{5} \left(6 - x\right)$

Then we add $\frac{4 x}{5}$ to both sides

$3 \left(x + 2\right) - x \le \frac{8}{5} \left(6 - x\right) + \frac{4 x}{5}$

Then we expand the bracket on the left

$3 x + 6 - x \le \frac{8}{5} \left(6 - x\right) + \frac{4 x}{5}$

Which is the same as

$2 x + 6 \le \frac{8}{5} \left(6 - x\right) + \frac{4 x}{5}$

Then multiply everything by $5$

$5 \left(2 x + 6\right) \le 8 \left(6 - x\right) + 4 x$

Then we expand the brackets again, this time on both sides

$10 x + 30 \le 48 - 8 x + 4 x$

Which is the same as

$10 x + 30 \le 48 - 4 x$

Now we add $4 x$ to both sides

$14 x + 30 = 48$

Then we take $30$ from both sides

$14 x = 18$

Finally we divide both sides by $14$

$x = \frac{18}{14}$

$x = \frac{9}{7}$