Question
11. If \( \frac{x}{5}=2-\frac{x}{4} \), then \( x= \)
Ask by Lang Bob. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = \frac{40}{9} \)
Solution
To solve the equation:
\[
\frac{x}{5} = 2 - \frac{x}{4}
\]
**Step 1: Eliminate the Fractions**
Find a common denominator to eliminate the fractions. The least common multiple of 5 and 4 is 20. Multiply both sides of the equation by 20:
\[
20 \left( \frac{x}{5} \right) = 20 \left( 2 - \frac{x}{4} \right)
\]
**Step 2: Simplify Both Sides**
\[
4x = 40 - 5x
\]
**Step 3: Solve for \( x \)**
Add \( 5x \) to both sides to get all terms containing \( x \) on one side:
\[
4x + 5x = 40
\]
\[
9x = 40
\]
Divide both sides by 9:
\[
x = \frac{40}{9}
\]
**Answer:**
\[
x = \boxed{\dfrac{40}{9}}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To solve the equation \( \frac{x}{5} = 2 - \frac{x}{4} \), first, eliminate the fractions by finding a common denominator, which is 20. Multiply the entire equation by 20: \[ 20 \cdot \frac{x}{5} = 20 \cdot \left(2 - \frac{x}{4}\right) \] This simplifies to: \[ 4x = 40 - 5x \] Now, add \( 5x \) to both sides: \[ 4x + 5x = 40 \] This gives: \[ 9x = 40 \] Now, divide by 9: \[ x = \frac{40}{9} \] So, the solution is \( x = \frac{40}{9} \).
