Pregunta
\( f(x)=\frac{1}{4} x-8 \) If \( f(X)=-\frac{7}{2} \), find \( X \)
Ask by Nunez Coleman. in the United Kingdom
Jan 23,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\( X = 18 \)
Solución
给定函数：
\[
f(x) = \frac{1}{4}x - 8
\]
当 \( f(X) = -\frac{7}{2} \) 时，求 \( X \)。
**解方程步骤如下：**
1. 代入已知值：
\[
\frac{1}{4}X - 8 = -\frac{7}{2}
\]
2. 将常数项移至方程右侧：
\[
\frac{1}{4}X = -\frac{7}{2} + 8
\]
3. 将8转换为分母为2的分数形式，方便计算：
\[
8 = \frac{16}{2}
\]
因此，
\[
\frac{1}{4}X = -\frac{7}{2} + \frac{16}{2} = \frac{9}{2}
\]
4. 乘以4以解出 \( X \)：
\[
X = \frac{9}{2} \times 4 = 18
\]
**最终答案：**
\[
X = 18
\]
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución Bonus Knowledge
To find \( X \), we need to set \( f(X) \) equal to \(-\frac{7}{2}\) and solve for \( X \). Starting with the function: \[ f(X) = \frac{1}{4}X - 8 \] Set \( f(X) \) equal to \(-\frac{7}{2}\): \[ \frac{1}{4}X - 8 = -\frac{7}{2} \] Next, add 8 to both sides: \[ \frac{1}{4}X = -\frac{7}{2} + 8 \] To simplify, convert 8 to a fraction with a denominator of 2: \[ 8 = \frac{16}{2} \] So, \[ -\frac{7}{2} + \frac{16}{2} = \frac{9}{2} \] Now we have: \[ \frac{1}{4}X = \frac{9}{2} \] To solve for \( X \), multiply both sides by 4: \[ X = 4 \times \frac{9}{2} = \frac{36}{2} = 18 \] Thus, the value of \( X \) is \( 18 \).
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