How do you solve \frac { x } { 3} = ( \frac { x } { 4} + 3)?

May 12, 2018

$x = 36$

Explanation:

To find the variable $x$, we need to make it alone. The first thing we do is multiply both sides by $\textcolor{b l u e}{3}$:
$\frac{x}{3} \quad \textcolor{b l u e}{\cdot \quad 3} = \left(\frac{x}{4} + 3\right) \quad \textcolor{b l u e}{\cdot \quad 3}$

$x = \frac{3 x}{4} + 9$

Now multiply both sides by $\textcolor{b l u e}{4}$ to get rid of the denominator:
$x \quad \textcolor{b l u e}{\cdot \quad 4} = \left(\frac{3 x}{4} + 9\right) \quad \textcolor{b l u e}{\cdot \quad 4}$

$4 x = 3 x + 36$

Now subtract $\textcolor{b l u e}{3 x}$ from both sides of the equation:
$4 x \quad \textcolor{b l u e}{- \quad 3 x} = 3 x + 36 \quad \textcolor{b l u e}{- \quad 3 x}$

Therefore,
$x = 36$

Hope this helps!