## Intermediate Algebra: Connecting Concepts through Application

$\color{blue}{\left\{-8, -3.8, 0, 4.5, 7.5\right\}}$
RECALL: Zero-Factor Property: If $ab = 0$, then either $a=0$ or $b=0$ or both are $0$. Use the property above to obtain: \begin{array}{cccccc} -2m=0 &\text{or} &m+3.8=0 &\text{or} &m-7.5=0 &\text{or} &2m-9=0 &\text{or}& m+8=0 \end{array} Solve each equation to obtain: $-2m=0 \\\frac{-2m}{-2}=\frac{0}{-2} \\m=0$ or $m+3.8=0 \\m=0-3.8 \\m=-3.8$ or $m-7.5=0 \\m=0+7.5 \\m=7.5$ or $2m-9=0 \\2m=0+9 \\2m=9 \\\frac{2m}{2} =\frac{9}{2} \\m=4.5$ or $m+8=0 \\m=0-8 \\m=-8$ Thus, the solution set is $\color{blue}{\left\{-8, -3.8, 0, 4.5, 7.5\right\}}$.