Question
Solve the equation \( \frac{1}{x}=\frac{5}{3 x}+8 \) \( x=\square \)
Ask by Bush Hammond. in the United States
Mar 03,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = -\frac{1}{12} \)
Solution
We start with the given equation:
1/x = (5/(3x)) + 8
Step 1: Multiply every term by the common denominator, 3x (note that x ≠ 0):
3x * (1/x) = 3x * (5/(3x)) + 3x * 8
Simplify each term:
3 = 5 + 24x
Step 2: Isolate x:
24x = 3 - 5
24x = -2
Divide both sides by 24:
x = -2/24
x = -1/12
Thus, the solution is:
x = -1/12
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Mind Expander
To solve the equation \( \frac{1}{x}=\frac{5}{3 x}+8 \), we first eliminate the fractions by multiplying through by \( 3x \): \[ 3 = 5 + 24x \] Now, we rearrange the equation: \[ 3 - 5 = 24x \] \[ -2 = 24x \] \[ x = -\frac{2}{24} \] \[ x = -\frac{1}{12} \] Therefore, the solution is \( x = -\frac{1}{12} \).
