Question
Solve for \( u \) \[ \frac{u}{2}-\frac{5}{6}=\frac{u}{3} \]
Ask by Sanders Colon. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( u = 5 \)
Solution
To solve the equation for \( u \):
\[
\frac{u}{2} - \frac{5}{6} = \frac{u}{3}
\]
**Step 1: eliminate the fractions**
Find the least common multiple (LCM) of the denominators \( 2 \), \( 3 \), and \( 6 \), which is \( 6 \). Multiply every term in the equation by \( 6 \) to eliminate the denominators:
\[
6 \cdot \frac{u}{2} - 6 \cdot \frac{5}{6} = 6 \cdot \frac{u}{3}
\]
**Step 2: simplify each term**
\[
3u - 5 = 2u
\]
**Step 3: isolate \( u \)**
Subtract \( 2u \) from both sides to get all \( u \) terms on one side:
\[
3u - 2u - 5 = 0
\]
\[
u - 5 = 0
\]
**Step 4: solve for \( u \)**
Add \( 5 \) to both sides:
\[
u = 5
\]
**Solution:**
\[
u = 5
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To solve the equation \( \frac{u}{2}-\frac{5}{6}=\frac{u}{3} \), we first want to eliminate the fractions. We can do this by finding a common denominator. The denominators here are 2, 3, and 6, and the least common multiple of these is 6. Let's multiply every term in the equation by 6: \[ 6 \left( \frac{u}{2} \right) - 6 \left( \frac{5}{6} \right) = 6 \left( \frac{u}{3} \right) \] This simplifies to: \[ 3u - 5 = 2u \] Next, we isolate \( u \) by subtracting \( 2u \) from both sides: \[ 3u - 2u - 5 = 0 \] \[ u - 5 = 0 \] Now, we add 5 to both sides to solve for \( u \): \[ u = 5 \] Thus, the solution is: \[ u = 5 \]
