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

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To find the value of $$ X $$ such that $$ f(X) = -\frac{7}{2} $$ for the function $$ f(x) = \frac{1}{4}x - 8 $$, follow these steps:

1. **Set up the equation:**
   $$
   \frac{1}{4}X - 8 = -\frac{7}{2}
   $$

2. **Eliminate the fraction by multiplying each term by 4:**
   $$
   4 \left( \frac{1}{4}X \right) - 4 \times 8 = 4 \times \left( -\frac{7}{2} \right)
   $$
   Simplifying this:
   $$
   X - 32 = -14
   $$

3. **Solve for $$ X $$:**
   $$
   X = -14 + 32
   $$
   $$
   X = 18
   $$

**Therefore, the value of $$ X $$ is 18.**

$$\boxed{18}$$
$$ X = 18 $$

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