Question
Solve for \( w \). \[ \frac{11 w}{10}-2=\frac{9 w}{8} \] Simplify, your answer as much as possible.
Ask by Guzman Martinez. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( w = -80 \)
Solution
To solve the equation for \( w \):
\[
\frac{11w}{10} - 2 = \frac{9w}{8}
\]
**Step 1: Eliminate the Fractions**
Find the least common multiple (LCM) of the denominators 10 and 8, which is 40. Multiply every term by 40 to eliminate the fractions:
\[
40 \times \left(\frac{11w}{10}\right) - 40 \times 2 = 40 \times \left(\frac{9w}{8}\right)
\]
**Step 2: Simplify Each Term**
\[
4 \times 11w - 80 = 5 \times 9w
\]
\[
44w - 80 = 45w
\]
**Step 3: Isolate \( w \)**
Subtract \( 44w \) from both sides:
\[
-80 = 45w - 44w
\]
\[
-80 = w
\]
**Solution:**
\[
w = -80
\]
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Simplify this solution Bonus Knowledge
To solve the equation \[ \frac{11 w}{10} - 2 = \frac{9 w}{8}, \] first, eliminate the fractions by finding a common denominator, which for 10 and 8 is 40. Multiply every term by 40: \[ 40 \cdot \left(\frac{11 w}{10}\right) - 40 \cdot 2 = 40 \cdot \left(\frac{9 w}{8}\right). \] This simplifies to: \[ 4 \cdot 11 w - 80 = 5 \cdot 9 w. \] Which further simplifies to: \[ 44 w - 80 = 45 w. \] Next, isolate \( w \) by getting all \( w \) terms on one side of the equation. Subtract \( 44 w \) from both sides: \[ -80 = 45 w - 44 w, \] which simplifies to: \[ -80 = w. \] Therefore, the solution is \[ w = -80. \]
