Question
\( f(x)=\frac{1}{4} x-8 \) If \( f(X)=-\frac{7}{2} \), find \( X \)
Ask by Martin Carter. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( X = 18 \)
Solution
To find the value of \( X \) when \( f(X) = -\frac{7}{2} \), we'll solve the equation step by step.
Given:
\[
f(X) = \frac{1}{4}X - 8
\]
And:
\[
f(X) = -\frac{7}{2}
\]
Set the two expressions for \( f(X) \) equal to each other:
\[
\frac{1}{4}X - 8 = -\frac{7}{2}
\]
**Step 1: Isolate the term with \( X \)**
\[
\frac{1}{4}X = -\frac{7}{2} + 8
\]
Convert 8 to a fraction with denominator 2 to combine the terms:
\[
8 = \frac{16}{2}
\]
So,
\[
\frac{1}{4}X = -\frac{7}{2} + \frac{16}{2} = \frac{9}{2}
\]
**Step 2: Solve for \( X \)**
\[
X = \frac{9}{2} \times 4 = 18
\]
**Answer:** \( X = 18 \)
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Extra Insights
To find \( X \), we start with the equation \( f(X) = -\frac{7}{2} \). Substituting into the function gives us: \[ -\frac{7}{2} = \frac{1}{4} X - 8 \] Next, we'll add 8 to both sides: \[ -\frac{7}{2} + 8 = \frac{1}{4} X \] Since 8 is the same as \( \frac{16}{2} \), we can combine the fractions: \[ -\frac{7}{2} + \frac{16}{2} = \frac{9}{2} \] Now, we have: \[ \frac{9}{2} = \frac{1}{4} X \] To solve for \( X \), we'll multiply both sides by 4: \[ 4 \cdot \frac{9}{2} = X \] Calculating this gives us: \[ X = 18 \] So, the solution is \( X = 18 \).
