Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$t=\left\{ -4,-\dfrac{10}{9} \right\}$
$\bf{\text{Solution Outline:}}$ 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, $t=\left\{ -4,-\dfrac{10}{9} \right\} .$