Solve for \(m\) in \(\frac{m-5}{2}\times \frac{-5-3}{5}=\frac{1}{2}\).
Solve for \(m\).
\[\frac{m-5}{2}\times \frac{-5-3}{5}=\frac{1}{2}\]
Simplify \(-5-3\) to \(-8\).
\[\frac{m-5}{2}\times \frac{-8}{5}=\frac{1}{2}\]
Simplify \(\frac{m-5}{2}\times \frac{-8}{5}\) to \(\frac{-8(m-5)}{10}\).
\[\frac{-8(m-5)}{10}=\frac{1}{2}\]
Move the negative sign to the left.
\[-\frac{8(m-5)}{10}=\frac{1}{2}\]
Simplify \(\frac{8(m-5)}{10}\) to \(\frac{4(m-5)}{5}\).
\[-\frac{4(m-5)}{5}=\frac{1}{2}\]
Multiply both sides by \(5\).
\[-4(m-5)=\frac{1}{2}\times 5\]
Simplify \(\frac{1}{2}\times 5\) to \(\frac{5}{2}\).
\[-4(m-5)=\frac{5}{2}\]
Divide both sides by \(-4\).
\[m-5=-\frac{\frac{5}{2}}{4}\]
Simplify \(\frac{\frac{5}{2}}{4}\) to \(\frac{5}{2\times 4}\).
\[m-5=-\frac{5}{2\times 4}\]
Simplify \(2\times 4\) to \(8\).
\[m-5=-\frac{5}{8}\]
Add \(5\) to both sides.
\[m=-\frac{5}{8}+5\]
Simplify \(-\frac{5}{8}+5\) to \(\frac{35}{8}\).
\[m=\frac{35}{8}\]
Substitute \(m=\frac{35}{8}\) into \(m-5-5-3=1\).
Since \(-\frac{69}{8}=1\) is not true, this is an inconsistent system.
