Answer
$t=\left\{ -\dfrac{1}{7},\dfrac{7}{3} \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|5t-3|=2t+4
,$ use the definition of an absolute value equality.
$\bf{\text{Solution Details:}}$
Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
5t-3=2t+4
\\\\\text{OR}\\\\
5t-3=-(2t+4)
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
5t-3=2t+4
\\\\
5t-2t=4+3
\\\\
3t=7
\\\\
t=\dfrac{7}{3}
\\\\\text{OR}\\\\
5t-3=-(2t+4)
\\\\
5t-3=-2t-4
\\\\
5t+2t=-4+3
\\\\
7t=-1
\\\\
t=-\dfrac{1}{7}
.\end{array}
Hence, $
t=\left\{ -\dfrac{1}{7},\dfrac{7}{3} \right\}
.$
