Solve for \(x\) in \(15\times 22\times 2x+\frac{5}{3}=\frac{26}{3}-x\).
Solve for \(x\).
\[15\times 22\times 2x+\frac{5}{3}=\frac{26}{3}-x\]
Simplify \(15\times 22\times 2x\) to \(660x\).
\[660x+\frac{5}{3}=\frac{26}{3}-x\]
Subtract \(\frac{5}{3}\) from both sides.
\[660x=\frac{26}{3}-x-\frac{5}{3}\]
Simplify \(\frac{26}{3}-x-\frac{5}{3}\) to \(7-x\).
\[660x=7-x\]
Add \(x\) to both sides.
\[660x+x=7\]
Simplify \(660x+x\) to \(661x\).
\[661x=7\]
Divide both sides by \(661\).
\[x=\frac{7}{661}\]
\[x=\frac{7}{661}\]
Substitute \(x=\frac{7}{661}\) into \(5x+\frac{7}{2}=\frac{3x}{2}-14\times 23\times 2x\times 3xL\).
Start with the original equation.
\[5x+\frac{7}{2}=\frac{3x}{2}-14\times 23\times 2x\times 3xL\]
Let \(x=\frac{7}{661}\).
\[5\times \frac{7}{661}+\frac{7}{2}=\frac{3\times \frac{7}{661}}{2}-14\times 23\times 2\times \frac{7}{661}\times 3xL\]
Simplify.
\[\frac{4697}{1322}=\frac{21}{1322}-\frac{13524xL}{661}\]
\[\frac{4697}{1322}=\frac{21}{1322}-\frac{13524xL}{661}\]
Since \(\frac{4697}{1322}=\frac{21}{1322}-\frac{13524xL}{661}\) is not true, this is an inconsistent system.
