Answer
The solutions are $x = 10$ and $x = -10$.
Work Step by Step
Use the rule $|x|=a \implies x=a \text{ or } x=-a$ to obtain:
$4x = 40$ or $4x = -40$
Now solve each equation.
For the first equation:
$4x = 40$
Divide both sides of the equation by $4$ to solve for $x$:
$x = 10$
For the second equation:
$4x = -40$
Divide both sides of the equation by $4$ to solve for $x$:
$x = -10$
Checking:
For $x=-10$:
\begin{align*}
|4(-10)|&=40\\
|-40|&=40\\
40&=40\\
\end{align*}
For $x=10$:
\begin{align*}
|4(10)|&=40\\
|40|&=40\\
40&=40\\
\end{align*}
Thus, the solutions are $x = 10$ and $x = -10$.
