# How do you solve \frac { 1} { 4} ( x + 6) = \frac { 1} { 6} ( x + 8)?

Mar 7, 2018

The solution is $x = - 2$.

#### Explanation:

Multiply both sides by $4$ and then $3$ to cancel out the fractions. Then, use the distributive property to get like terms and isolate $x$:

$\frac{1}{4} \left(x + 6\right) = \frac{1}{6} \left(x + 8\right)$

$\textcolor{b l u e}{4 \cdot} \frac{1}{4} \left(x + 6\right) = \textcolor{b l u e}{4 \cdot} \frac{1}{6} \left(x + 8\right)$

$\textcolor{red}{\cancel{\textcolor{b l a c k}{\textcolor{b l u e}{4 \cdot} \frac{1}{4}}}} \left(x + 6\right) = \textcolor{b l u e}{4 \cdot} \frac{1}{6} \left(x + 8\right)$

$x + 6 = \frac{\textcolor{b l u e}{4}}{6} \left(x + 8\right)$

$x + 6 = \frac{\textcolor{b l u e}{2}}{3} \left(x + 8\right)$

$\textcolor{b l u e}{3 \cdot} \left(x + 6\right) = \textcolor{b l u e}{3 \cdot} \frac{\textcolor{b l u e}{2}}{3} \left(x + 8\right)$

$\textcolor{b l u e}{3 \cdot} \left(x + 6\right) = \textcolor{b l u e}{\textcolor{red}{\cancel{\textcolor{b l u e}{3}}} \cdot} \frac{\textcolor{b l u e}{2}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} \left(x + 8\right)$

$\textcolor{b l u e}{3} \cdot \left(x + 6\right) = \textcolor{b l u e}{2} \cdot \left(x + 8\right)$

$\textcolor{b l u e}{3} x + \textcolor{b l u e}{3} \cdot 6 = \textcolor{b l u e}{2} x + \textcolor{b l u e}{2} \cdot 8$

$\textcolor{b l u e}{3} x + \textcolor{b l u e}{18} = \textcolor{b l u e}{2} x + \textcolor{b l u e}{16}$

Now, subtract $2 x$ from both sides, then $18$:

$3 x + 18 = 2 x + 16$

$3 x + 18 \textcolor{b l u e}{-} \textcolor{b l u e}{2 x} = 2 x + 16 \textcolor{b l u e}{-} \textcolor{b l u e}{2 x}$

$3 x \textcolor{b l u e}{-} \textcolor{b l u e}{2 x} + 18 = 2 x - \textcolor{b l u e}{2 x} + 16$

$x + 18 = \textcolor{red}{\cancel{\textcolor{b l a c k}{2 x - \textcolor{b l u e}{2 x}}}} + 16$

$x + 18 = 16$

$x + 18 \textcolor{b l u e}{-} \textcolor{b l u e}{18} = 16 \textcolor{b l u e}{-} \textcolor{b l u e}{18}$

$x \textcolor{red}{\cancel{\textcolor{b l a c k}{+ 18 \textcolor{b l u e}{-} \textcolor{b l u e}{18}}}} = 16 \textcolor{b l u e}{-} \textcolor{b l u e}{18}$

$x = 16 - 18$

$x = - 2$