# What is the value of x in the equation (3/4)x + 2 = (5/4)x - 6 ?

Apr 17, 2018

$x = 16$

#### Explanation:

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

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

$8 = \frac{1}{2} x$

$x = 16$

Apr 17, 2018

$x = 16$

#### Explanation:

Re-arrange the equation.

Add $6$ to both sides:

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

Multiply out $\left(\frac{3}{4}\right) x \text{ and } \left(\frac{5}{4}\right) x$:

$\frac{3 x}{4}$ and $\frac{5 x}{4}$

Multiply it all by 4:

$3 x + 8 \left(4\right) = 5 x$

Solve:

$3 x - 3 x + 32 = 5 x - 3 x$
$32 = 2 x$

$x = 16$

Apr 17, 2018

$x = 16$

#### Explanation:

$\text{collect terms in x on one side of the equation and}$
$\text{numeric values on the other side}$

$\text{subtract "3/4x" from both sides}$

$\cancel{\frac{3}{4} x} \cancel{- \frac{3}{4} x} + 2 = \frac{5}{4} x - \frac{3}{4} x - 6$

$\Rightarrow 2 = \frac{1}{2} x - 6$

$\text{add 6 to both sides}$

$2 + 6 = \frac{1}{2} x \cancel{- 6} \cancel{+ 6}$

$\Rightarrow 8 = \frac{1}{2} x$

$\text{multiply both sides by 2}$

$\Rightarrow x = 16 \text{ is the solution}$