We are given: \((\frac{x}{4})+(\frac{1}{2})=\frac{1}{8}\)

Multiply both sides by the LCD which is 8: \(((\frac{x}{4})+(\frac{1}{2}))(8)=\frac{1}{8}(8)\)

\(2x+4=1\)

Subtract 4 from both sides: \(2x+4-4=1-4\)

\(2x=-3\)

Divide both sides by 2: \(\frac{2x}{2}=-\frac{3}{2}\)

\(x=-(\frac{3}{2})\)