Simplify \(\frac{\frac{x}{2}+\frac{3}{4}}{6}\) to \(\frac{\frac{x}{2}}{6}+\frac{\frac{3}{4}}{6}\).
\[\frac{\frac{x}{2}}{6}+\frac{\frac{3}{4}}{6}=\frac{x}{2}+\frac{1}{3}\]
Simplify \(\frac{\frac{x}{2}}{6}\) to \(\frac{x}{2\times 6}\).
\[\frac{x}{2\times 6}+\frac{\frac{3}{4}}{6}=\frac{x}{2}+\frac{1}{3}\]
Simplify \(2\times 6\) to \(12\).
\[\frac{x}{12}+\frac{\frac{3}{4}}{6}=\frac{x}{2}+\frac{1}{3}\]
Simplify \(\frac{\frac{3}{4}}{6}\) to \(\frac{3}{4\times 6}\).
\[\frac{x}{12}+\frac{3}{4\times 6}=\frac{x}{2}+\frac{1}{3}\]
Simplify \(4\times 6\) to \(24\).
\[\frac{x}{12}+\frac{3}{24}=\frac{x}{2}+\frac{1}{3}\]
Simplify \(\frac{3}{24}\) to \(\frac{1}{8}\).
\[\frac{x}{12}+\frac{1}{8}=\frac{x}{2}+\frac{1}{3}\]
Multiply both sides by \(12\) (the LCM of \(12, 2\)).
\[x+\frac{3}{2}=6x+4\]
Subtract \(x\) from both sides.
\[\frac{3}{2}=6x+4-x\]
Simplify \(6x+4-x\) to \(5x+4\).
\[\frac{3}{2}=5x+4\]
Subtract \(4\) from both sides.
\[\frac{3}{2}-4=5x\]
Simplify \(\frac{3}{2}-4\) to \(-\frac{5}{2}\).
\[-\frac{5}{2}=5x\]
Divide both sides by \(5\).
\[-\frac{\frac{5}{2}}{5}=x\]
Simplify \(\frac{\frac{5}{2}}{5}\) to \(\frac{5}{2\times 5}\).
\[-\frac{5}{2\times 5}=x\]
Simplify \(2\times 5\) to \(10\).
\[-\frac{5}{10}=x\]
Simplify \(\frac{5}{10}\) to \(\frac{1}{2}\).
\[-\frac{1}{2}=x\]
Switch sides.
\[x=-\frac{1}{2}\]
Decimal Form: -0.5
x=-1/2
