Which value of x satisfies the equation \( \frac{1}{3}\left(x-\frac{1}{4}\right)=\frac{23}{12} \) ?

To solve the equation \( \frac{1}{3}\left(x-\frac{1}{4}\right)=\frac{23}{12} \), we start by eliminating the fraction on the left side. We can do this by multiplying both sides by 3: \[ x - \frac{1}{4} = 3 \cdot \frac{23}{12} \] Calculating the right-hand side: \[ 3 \cdot \frac{23}{12} = \frac{69}{12} \] Now we simplify \( \frac{69}{12} \): \[ \frac{69}{12} = \frac{23}{4} \quad \text{(by dividing the numerator and the denominator by 3)} \] So we have: \[ x - \frac{1}{4} = \frac{23}{4} \] Next, we add \( \frac{1}{4} \) to both sides: \[ x = \frac{23}{4} + \frac{1}{4} \] Combining the fractions on the right-hand side: \[ x = \frac{23 + 1}{4} = \frac{24}{4} = 6 \] Thus, the value of \( x \) that satisfies the equation is: \[ \boxed{6} \]