Answer
$t=\left\{ -4,-\dfrac{10}{9} \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|5t+7|=|4t+3|
,$ use the definition of absolute value equality. Then use the properties of equality 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}
5t+7=4t+3
\\\\\text{OR}\\\\
5t+7=-(4t+3)
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
5t+7=4t+3
\\\\
5t-4t=3-7
\\\\
t=-4
\\\\\text{OR}\\\\
5t+7=-(4t+3)
\\\\
5t+7=-4t-3
\\\\
5t+4t=-3-7
\\\\
9t=-10
\\\\
t=-\dfrac{10}{9}
.\end{array}
Hence, $
t=\left\{ -4,-\dfrac{10}{9} \right\}
.$
