Answer
$x=1$
Work Step by Step
The given equation, $
|2x+5|=3x+4
,$ is equivalent to
\begin{array}{l}\require{cancel}
2x+5=3x+4
\\\\\text{OR}\\\\
2x+5=-(3x+4)
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
2x+5=3x+4
\\
2x-3x=4-5
\\
-x=-1
\\
x=1
\\\\\text{OR}\\\\
2x+5=-(3x+4)
\\
2x+5=-3x-4
\\
2x+3x=-4-5
\\
5x=-9
\\
\dfrac{5x}{5}=-\dfrac{9}{5}
\\
x=-\dfrac{9}{5}
.\end{array}
Since the right side of the given equation is not a constant, then checking of solution/s is required.
Substituting $
x=1
$ in the original equation results to
\begin{array}{l}\require{cancel}
|2x+5|=3x+4
\\
|2(1)+5|=3(1)+4
\\
|2+5|=3+4
\\
|7|=7
\\
7=7
\text{ (TRUE)}
.\end{array}
Substituting $
x=-\dfrac{9}{5}
$ in the original equation results to
\begin{array}{l}\require{cancel}
|2x+5|=3x+4
\\
\left|2\left( -\dfrac{9}{5} \right)+5\right|=3\left( -\dfrac{9}{5} \right)+4
\\
\left|-\dfrac{18}{5}+5\right|= -\dfrac{27}{5}+4
\\
\left|-\dfrac{18}{5}+\dfrac{25}{5}\right|= -\dfrac{27}{5}+\dfrac{20}{5}
\\
\left|\dfrac{7}{5}\right|= -\dfrac{7}{5}
\\
\dfrac{7}{5}= -\dfrac{7}{5}
\text{ (FALSE)}
.\end{array}
Since the substitution above resulted in a FALSE statement, then $
x=-\dfrac{9}{5}
,$ is not a solution (an extraneous solution).
Hence, the solution is $
x=1
.$
