Solve for \(x\) in \(-\frac{8x}{100}+\frac{20000-x}{75}=800\).
Solve for \(x\).
\[-\frac{8x}{100}+\frac{20000-x}{75}=800\]
Simplify \(\frac{8x}{100}\) to \(\frac{2x}{25}\).
\[-\frac{2x}{25}+\frac{20000-x}{75}=800\]
Simplify using the common denominator.
\[\frac{-3\times 2x+20000-x}{75}=800\]
Simplify \(-3\times 2x\) to \(-6x\).
\[\frac{-6x+20000-x}{75}=800\]
Simplify \(-6x+20000-x\) to \(-7x+20000\).
\[\frac{-7x+20000}{75}=800\]
Multiply both sides by \(75\).
\[-7x+20000=800\times 75\]
Simplify \(800\times 75\) to \(60000\).
\[-7x+20000=60000\]
Subtract \(20000\) from both sides.
\[-7x=60000-20000\]
Simplify \(60000-20000\) to \(40000\).
\[-7x=40000\]
Divide both sides by \(-7\).
\[x=-\frac{40000}{7}\]
Substitute \(x=-\frac{40000}{7}\) into \(\frac{6x}{75}+\frac{20000-x}{75}=800\).
Start with the original equation.
\[\frac{6x}{75}+\frac{20000-x}{75}=800\]
Let \(x=-\frac{40000}{7}\).
\[\frac{6\times \frac{-40000}{7}}{75}+\frac{20000+\frac{40000}{7}}{75}=800\]
Simplify.
\[-\frac{800}{7}=800\]
Since \(-\frac{800}{7}=800\) is not true, this is an inconsistent system.
