Question
Solve for \( x \) : \( \frac{1}{5} x+\frac{1}{2}=1 \) You can enter your answer as an improper fraction (like 13/4), but not as a mixed number.
Ask by Cox Brooks. in the United States
Mar 16,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = \frac{5}{2} \)
Solution
1. Start with the equation:
\[
\frac{1}{5}x + \frac{1}{2} = 1
\]
2. Subtract \(\frac{1}{2}\) from both sides to isolate the term with \(x\):
\[
\frac{1}{5}x = 1 - \frac{1}{2}
\]
3. Simplify the right-hand side:
\[
1 - \frac{1}{2} = \frac{2}{2} - \frac{1}{2} = \frac{1}{2}
\]
So, the equation becomes:
\[
\frac{1}{5}x = \frac{1}{2}
\]
4. Multiply both sides by 5 to solve for \(x\):
\[
x = \frac{1}{2} \times 5 = \frac{5}{2}
\]
The solution is:
\[
\frac{5}{2}
\]
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Simplify this solution Mind Expander
To solve for \( x \) in the equation \( \frac{1}{5} x + \frac{1}{2} = 1 \), start by isolating \( x \). First, subtract \( \frac{1}{2} \) from both sides: \[ \frac{1}{5} x = 1 - \frac{1}{2} \] Now, \( 1 - \frac{1}{2} \) equals \( \frac{1}{2} \), so we have: \[ \frac{1}{5} x = \frac{1}{2} \] Next, multiply both sides by 5 to eliminate the fraction: \[ x = 5 \times \frac{1}{2} \] This simplifies to: \[ x = \frac{5}{2} \] Thus, the solution is \( x = \frac{5}{2} \).
