Answer
$x=3$
Work Step by Step
The given equation is
$\Rightarrow |2+x|=|x-8|$
Write related linear equations.
$\Rightarrow 2+x=x-8$ or $2+x=−(x-8)$
Solve the first equation.
$\Rightarrow 2+x=x-8$
Add $8$ to each side.
$\Rightarrow 2+x+8=x-8+8$
Simplify.
$\Rightarrow 10+x=x$
Subtract $x$ from each side.
$\Rightarrow 10+x-x=x-x$
Simplify.
$\Rightarrow 10=0$
Which is false statement.
Solve the second equation.
$\Rightarrow 2+x=-(x-8)$
Clear the parentheses.
$\Rightarrow 2+x=-x+8$
Add $x$ to each side.
$\Rightarrow 2+x+x=-x+8+x$
Simplify.
$\Rightarrow 2+2x=8$
Subtract $2$ from each side.
$\Rightarrow 2+2x-2=8-2$
Simplify.
$\Rightarrow 2x=6$
Divide each side by $2$.
$\Rightarrow \frac{2x}{2}=\frac{6}{2}$
Simplify.
$\Rightarrow x=3$
Check $x=3$
$\Rightarrow |2+3|=|3-8|$
$\Rightarrow |5|=|-5|$
$\Rightarrow 5=5$
True.
Hence, the solution is $x=3$.
