OpenStudy (anonymous):

5(m + 4) = 2(m + 2) +4

5 years ago
OpenStudy (anonymous):

\[\large 5(m + 4) = 2(m + 2) +4\] Distributive property- distribute the \(5\) to \((m+4)\) and the \(2\) to \((m+2)\):\[5(m + 4) = 2(m + 2) +4\]\[(\color{blue}{5\times} m+\color{blue}{5\times}4)=(\color{blue}{2\times} m+\color{blue}{2\times}2)+4\]\[\implies~~~\color{red}{5m}+\color{red}{20}=\color{red}{2m}+\color{red}{4}+4\]Add/Combine like terms:\[5m+20=2m+4+4\]\[5m+20=2m+\color{red}{8}\]Subtraction Property of Equality- subtract \(20\) from both sides:\[5m+20=2m+8\]\[5m+20\color{blue}{-20}=2m+8\color{blue}{-20}\]\[\implies~5m+\color{red}{0}=2m\color{red}{-12}\]Subtraction Property of Equality- subtract \(2m\) from both sides:\[5m=2m-12\]\[5m\color{blue}{-2m}=2m\color{blue}{-2m}-12\]\[\implies~\color{red}{3m}=\color{red}{0}-12\]Division Property of Equality- divide both sides by \(3\):\[3m=-12\]\[{3m\over{\color{blue}{3}}}={-12\over{\color{blue}{3}}}\]\[\implies~\color{red}{m}=\color{red}{-4}\] \[\large\color{purple}{m=-4}\]

5 years ago