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

Question

UpStudy AI · Accepted Answer

To solve the equation:

$$
\frac{x}{5} = 2 - \frac{x}{4}
$$

**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:**

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

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