# How do you solve for M in -0.50=(47-M)/(56-M)?

Jan 10, 2017

$M = 50$

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{56 - M}$ to eliminate the fraction:

$- 0.50 \times \left(\textcolor{red}{56 - M}\right) = \frac{47 - M}{56 - M} \times \left(\textcolor{red}{56 - M}\right)$

$- 28 + \left(0.50 \times - M\right) = \frac{47 - M}{\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(56 - M\right)}}}} \times \cancel{\left(\textcolor{red}{56 - M}\right)}$

$- 28 + \left(0.50 M\right) = 47 - M$

$- 28 + \left(0.50 M\right) + \textcolor{b l u e}{28} + \textcolor{red}{M} = 47 - M + \textcolor{b l u e}{28} + \textcolor{red}{M}$

$- 28 + \textcolor{b l u e}{28} + \left(0.50 M\right) + \textcolor{red}{M} = 47 + \textcolor{b l u e}{28} - M + \textcolor{red}{M}$

$0 + 1.50 M = 75 - 0$

$1.50 M = 75$

$\frac{1.50 M}{\textcolor{red}{1.50}} = \frac{75}{\textcolor{red}{1.50}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{1.50}}} M}{\cancel{\textcolor{red}{1.50}}} = 50$

$M = 50$