Question
\( f(x)=\frac{1}{4} x-8 \) If \( f(X)=-\frac{7}{2} \), find \( X \)
Ask by Sherman Chavez. in Greenland
Feb 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( X = 18 \)
Solution
Given the function f(x) = (1/4)x - 8, we need to find X when f(X) = -7/2.
Step 1: Write the equation with X:
(1/4)X - 8 = -7/2
Step 2: Multiply every term by 4 to eliminate the fraction:
X - 32 = -14
Step 3: Solve for X by adding 32 to both sides:
X = -14 + 32
X = 18
Thus, the value of X is 18.
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Simplify this solution Extra Insights
To solve for \( X \) in the equation \( f(X) = -\frac{7}{2} \), we start by substituting \(-\frac{7}{2}\) into the function: \[ -\frac{7}{2} = \frac{1}{4} X - 8 \] Next, we add 8 to both sides. To add 8, we convert it to a fraction with a denominator of 2: \[ -\frac{7}{2} + \frac{16}{2} = \frac{1}{4} X \] \[ \frac{9}{2} = \frac{1}{4} X \] Now, to eliminate \(\frac{1}{4}\), we multiply both sides by 4: \[ 4 \cdot \frac{9}{2} = X \] \[ X = \frac{36}{2} = 18 \] Thus, the value of \( X \) is: \[ X = 18 \]
