How do you solve -x/4 = (2x)/3?

Mar 10, 2018

$0 = x$

Explanation:

$- \frac{x}{4} = \frac{2 x}{3} | + \frac{x}{4}$
$0 = \frac{2 x}{3} + \frac{x}{4}$
$0 = \frac{11 x}{12} | \cdot \frac{12}{11}$
$0 = x$

Mar 10, 2018

See a solution process below:

Explanation:

First, multiply each side of the equation by $\textcolor{red}{12}$ to eliminate the fractions while keeping the equation balanced:

$\textcolor{red}{12} \times - \frac{x}{4} = \textcolor{red}{12} \times \frac{2 x}{3}$

$\cancel{\textcolor{red}{12}} \textcolor{red}{3} \times - \frac{x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}} = \cancel{\textcolor{red}{12}} \textcolor{red}{4} \times \frac{2 x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}}$

$\textcolor{red}{3} \times - x = \textcolor{red}{4} \times 2 x$

$- 3 x = 8 x$

Next, add $\textcolor{red}{3 x}$ to each side of the equation to isolate the $x$ term while keeping the equation balanced:

$- 3 x + \textcolor{red}{3 x} = 8 x + \textcolor{red}{3 x}$

$0 = \left(8 + \textcolor{red}{3}\right) x$

$0 = 11 x$

Now, divide each side of the equation by $\textcolor{red}{11}$ to solve for $x$ while keeping the equation balanced:

$\frac{0}{\textcolor{red}{11}} = \frac{11 x}{\textcolor{red}{11}}$

$0 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{11}}} x}{\cancel{\textcolor{red}{11}}}$

$0 = x$

$x = 0$