Question
Solve the equation. \( \frac{1}{4} x=\frac{3}{20} \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \( \} \). (Type an integer or a simplified fraction.) B. There is no solution.
Ask by Greene Dunn. in the United States
Jan 20,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The solution is \( x = \frac{3}{5} \).
Solution
To solve the equation:
\[
\frac{1}{4} x = \frac{3}{20}
\]
**Step 1:** Multiply both sides by 4 to isolate \( x \):
\[
x = 4 \times \frac{3}{20}
\]
**Step 2:** Simplify the multiplication:
\[
x = \frac{12}{20}
\]
**Step 3:** Reduce the fraction to its simplest form:
\[
x = \frac{3}{5}
\]
**Conclusion:**
The correct choice is:
**A. The solution set is \( \left\{ \frac{3}{5} \right\} \).**
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Extra Insights
To solve the equation \( \frac{1}{4} x = \frac{3}{20} \), you can start by multiplying both sides by 4 to eliminate the fraction: \[ x = 4 \cdot \frac{3}{20} \] This simplifies to: \[ x = \frac{12}{20} = \frac{3}{5} \] So, the solution set is \( \{ \frac{3}{5} \} \). Therefore, the correct choice is: A. The solution set is \( \{ \frac{3}{5} \} \).