Simplify \(x+7-8x\) to \(-7x+7\).
\[\frac{-7x+7}{83}=\frac{17}{6}-\frac{5x}{2}\]
Factor out the common term \(7\).
\[\frac{-7(x-1)}{83}=\frac{17}{6}-\frac{5x}{2}\]
Move the negative sign to the left.
\[-\frac{7(x-1)}{83}=\frac{17}{6}-\frac{5x}{2}\]
Multiply both sides by \(166\) (the LCM of \(83, 2\)).
\[-14(x-1)=\frac{1411}{3}-415x\]
Expand.
\[-14x+14=\frac{1411}{3}-415x\]
Subtract \(14\) from both sides.
\[-14x=\frac{1411}{3}-415x-14\]
Simplify \(\frac{1411}{3}-415x-14\) to \(-415x+\frac{1369}{3}\).
\[-14x=-415x+\frac{1369}{3}\]
Add \(415x\) to both sides.
\[-14x+415x=\frac{1369}{3}\]
Simplify \(-14x+415x\) to \(401x\).
\[401x=\frac{1369}{3}\]
Divide both sides by \(401\).
\[x=\frac{\frac{1369}{3}}{401}\]
Simplify \(\frac{\frac{1369}{3}}{401}\) to \(\frac{1369}{3\times 401}\).
\[x=\frac{1369}{3\times 401}\]
Simplify \(3\times 401\) to \(1203\).
\[x=\frac{1369}{1203}\]
Decimal Form: 1.137988
x=1369/1203
