Answer
$x=-\dfrac{1}{2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|x+4|=|x-3|
,$ use the definition of absolute equality. Then use the properties of anequality to isolate the variable.
$\bf{\text{Solution Details:}}$
Since $|x|=|y|$ implies $x=y \text{ or } x=-y,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
x+4=x-3
\\\\\text{OR}\\\\
x+4=-(x-3)
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
x+4=x-3
\\\\
x-x=-3-4
\\\\
0=-7
\text{ (FALSE)}
\\\\\text{OR}\\\\
x+4=-(x-3)
\\\\
x+4=-x+3
\\\\
x+x=3-4
\\\\
2x=-1
\\\\
x=-\dfrac{1}{2}
.\end{array}
Hence, $
x=-\dfrac{1}{2}
.$
