Answer
$x=-1$
Work Step by Step
The given equation is
$\Rightarrow |x-2|=|4+x|$
Write related linear equations.
$\Rightarrow x-2=4+x$ or $x-2=−(4+x)$
Solve the first equation.
$\Rightarrow x-2=4+x$
Add $2$ to each side.
$\Rightarrow x-2+2=4+x+2$
Simplify.
$\Rightarrow x=6+x$
Subtract $x$ from each side.
$\Rightarrow x-x=6+x-x$
Simplify.
$\Rightarrow 0=6$
Which is false statement.
Solve the second equation.
$\Rightarrow x-2=−(4+x)$
Clear the parentheses.
$\Rightarrow x-2=−4-x$
Add $2$ to each side.
$\Rightarrow x-2+2=-4-x+2$
Simplify.
$\Rightarrow x=-2-x$
Add $x$ to each side.
$\Rightarrow x+x=-2-x+x$
Simplify.
$\Rightarrow 2x=-2$
Divide each side by $2$.
$\Rightarrow \frac{2x}{2}=-\frac{2}{2}$
Simplify.
$\Rightarrow x=-1$
Check $x=-1$
$\Rightarrow |-1-2|=|4-1|$
$\Rightarrow |-3|=|3|$
$\Rightarrow 3=3$
True.
Hence, the solution is $x=-1$.
