Answer
$x=-\frac{1}{5}$
Work Step by Step
The given equation is
$\Rightarrow |5x-2|=|5x+4|$
Write related linear equations.
$\Rightarrow 5x-2=5x+4$ or $5x-2=−(5x+4)$
Solve the first equation.
$\Rightarrow 5x-2=5x+4$
Add $2$ to each side.
$\Rightarrow 5x-2+2=5x+4+2$
Simplify.
$\Rightarrow 5x=5x+6$
Subtract $5x$ from each side.
$\Rightarrow 5x-5x=5x+6-5x$
Simplify.
$\Rightarrow =6$
Which is false statement.
Solve the second equation.
$\Rightarrow 5x-2=−(5x+4)$
Clear the parentheses.
$\Rightarrow 5x-2=−5x-4$
Add $5x$ to each side.
$\Rightarrow 5x-2+5x=−5x-4+5x$
Simplify.
$\Rightarrow 10x-2=-4$
Add $2$ to each side.
$\Rightarrow 10x-2+2=-4+2$
Simplify.
$\Rightarrow 10x=-2$
Divide each side by $10$.
$\Rightarrow \frac{10x}{10}=-\frac{2}{10}$
Simplify.
$\Rightarrow x=-\frac{1}{5}$
Check $x=-\frac{1}{5}$.
$\Rightarrow |5(-\frac{1}{5})-2|=|5(-\frac{1}{5})+4|$
$\Rightarrow |-1-2|=|-1+4|$
$\Rightarrow |-3|=|3|$
$\Rightarrow 3=3$
True.
Hence, the solution is $x=-\frac{1}{5}$.
