\( f(x)=\frac{1}{4} x-8 \) If \( f(X)=-\frac{7}{2} \), find \( X \)

To find \( X \), we start by setting the equation for \( f(x) \) equal to \(-\frac{7}{2}\): \[ \frac{1}{4} X - 8 = -\frac{7}{2} \] Next, we solve for \( X \). First, add 8 to both sides: \[ \frac{1}{4} X = -\frac{7}{2} + 8 \] Convert 8 into halves: \[ 8 = \frac{16}{2} \] Now, combine the fractions: \[ -\frac{7}{2} + \frac{16}{2} = \frac{9}{2} \] So now our equation looks like this: \[ \frac{1}{4} X = \frac{9}{2} \] To isolate \( X \), multiply both sides by 4: \[ X = 4 \cdot \frac{9}{2} = \frac{36}{2} = 18 \] Thus, the solution is: \[ X = 18 \]