How do you solve (-11x+5)/ 6=-1/2?

Mar 3, 2018

$x = \frac{8}{11}$

Explanation:

$\frac{- 11 x + 5}{6} = - \frac{1}{2}$

$\frac{- 11 x + 5}{6} \textcolor{b l u e}{\cdot 6} = - \frac{1}{2} \textcolor{b l u e}{\cdot 6}$

$\frac{- 11 x + 5}{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}}} \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{6}}} = - \frac{1}{2} \cdot 6$

$- 11 x + 5 = - \frac{6}{2}$

$- 11 x + 5 = - 3$

$- 11 x + 5 \textcolor{b l u e}{- 5} = - 3 \textcolor{b l u e}{- 5}$

$- 11 x \textcolor{red}{\cancel{\textcolor{b l a c k}{+ 5 - 5}}} = - 3 - 5$

$- 11 x = - 8$

$\frac{- 11 x}{\textcolor{b l u e}{- 11}} = \frac{- 8}{\textcolor{b l u e}{- 11}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 11}}} x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 11}}}} = \frac{- 8}{- 11}$

$x = \frac{8}{11}$

That is the answer. We can make sure that it is correct by plugging it into the original equation:

$\textcolor{w h i t e}{\implies} \frac{- 11 x + 5}{6} = - \frac{1}{2}$

$\implies \frac{- 11 \left(\frac{8}{11}\right) + 5}{6} = - \frac{1}{2}$

$\textcolor{w h i t e}{\implies} \frac{- \textcolor{red}{\cancel{\textcolor{b l a c k}{11}}} \left(\frac{8}{\textcolor{red}{\cancel{\textcolor{b l a c k}{11}}}}\right) + 5}{6} = - \frac{1}{2}$

$\frac{- 8 + 5}{6} = - \frac{1}{2}$

$\frac{- 3}{6} = - \frac{1}{2}$

-1/2=-1/2 qquadcolor(lightgreen)sqrt

Since this statement is true, our answer is correct.