Answer
$x=7$ and $x=−3$
Work Step by Step
The given equation is
$\Rightarrow |x+8|=|2x+1|$
Write related linear equations.
$\Rightarrow x+8=2x+1$ or $x+8=−(2x+1)$
Solve the first equation.
$\Rightarrow x+8=2x+1$
Add $-1-x$ to each side.
$\Rightarrow x+8-1-x=2x+1-1-x$
Simplify.
$\Rightarrow 7=x$
Solve the second equation.
$\Rightarrow x+8=-(2x+1)$
Clear the parentheses.
$\Rightarrow x+8=-2x-1$
Add $2x-8$ to each side.
$\Rightarrow x+8+2x-8=-2x-1+2x-8$
Simplify.
$\Rightarrow 3x=-9$
Divide each side by $3$.
$\Rightarrow \frac{3x}{3}=-\frac{9}{3}$
Simplify.
$\Rightarrow x=-3$
Check $x=7$
$\Rightarrow |7+8|=|2(7)+1|$
$\Rightarrow |15|=|14+1|$
$\Rightarrow |15|=|15|$
$\Rightarrow 15=15$
True.
Check $x=-3$
$\Rightarrow |-3+8|=|2(-3)+1|$
$\Rightarrow |5|=|-6+1|$
$\Rightarrow |5|=|-5|$
$\Rightarrow 5=5$
True.
Hence, the solutions are $x=7$ and $x=−3$.
