11. If $$ \frac{x}{5}=2-\frac{x}{4} $$, then $$ x= $$

Question

UpStudy AI · Accepted Answer

To solve the equation $$ \frac{x}{5} = 2 - \frac{x}{4} $$, follow these steps:

1. **Multiply both sides by 20** (the least common multiple of 5 and 4) to eliminate the denominators:

$$
   20 \cdot \frac{x}{5} = 20 \cdot \left(2 - \frac{x}{4}\right)
   $$

2. **Simplify each term**:

$$
   4x = 40 - 5x
   $$

3. **Combine like terms** by adding $$ 5x $$ to both sides:

$$
   4x + 5x = 40
   $$
   
   $$
   9x = 40
   $$

4. **Solve for $$ x $$** by dividing both sides by 9:

$$
   x = \frac{40}{9}
   $$

So, the solution is:

$$
x = \frac{40}{9}
$$

This can also be expressed as a mixed number:

$$
x = 4 \frac{4}{9}
$$

Or as a decimal:

$$
x \approx 4.444\ldots
$$

**Answer:** $$ x = \dfrac{40}{9} $$
$$ x = \frac{40}{9} $$

11. If \( \frac{x}{5}=2-\frac{x}{4} \), then \( x= \)