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

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We start with the equation $$ f(x)=\frac{1}{4} x-8 $$ and substitute $$ x=X $$ and $$ f(X)=-\frac{7}{2} $$. This gives us $$ \frac{1}{4} X - 8 = -\frac{7}{2} $$.
Add $$ 8 $$ to both sides to isolate the term with $$ X $$:$$
\frac{1}{4} X = -\frac{7}{2} + 8
$$
Convert $$ 8 $$ to a fraction with denominator 2: $$ 8 = \frac{16}{2} $$. Now,$$
\frac{1}{4} X = -\frac{7}{2} + \frac{16}{2} = \frac{9}{2}
$$
Multiply both sides by 4 to eliminate the fraction: $$
X = 4 \times \frac{9}{2} = \frac{36}{2} = 18
$$
The value of $$ X $$ is $$ 18 $$.

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