To solve the equation \(x - \frac{1}{4} = \frac{1}{2}\) for \(x\), we need to isolate \(x\) on one side of the equation.
First, let's add \(\frac{1}{4}\) to both sides of the equation to get rid of the \(-\frac{1}{4}\) term:
\[x - \frac{1}{4} + \frac{1}{4} = \frac{1}{2} + \frac{1}{4}\]
Simplify:
\[x = \frac{1}{2} + \frac{1}{4}\]
To add the fractions \(\frac{1}{2}\) and \(\frac{1}{4}\), we need to find a common denominator, which is \(4\):
\[x = \frac{2}{4} + \frac{1}{4}\]
Now, add the fractions:
\[x = \frac{2 + 1}{4}\]
\[x = \frac{3}{4}\]
So, the solution to the equation \(x - \frac{1}{4} = \frac{1}{2}\) is \(x = \frac{3}{4}\).
