j) $$ \frac{x}{2}+\frac{x}{3}=5 $$

Question

UpStudy AI · Accepted Answer

To solve the equation:

$$
\frac{x}{2} + \frac{x}{3} = 5
$$

**Step 1: Find a Common Denominator**

The denominators are 2 and 3. The least common denominator (LCD) is 6. Multiply each term of the equation by 6 to eliminate the fractions:

$$
6 \left( \frac{x}{2} \right) + 6 \left( \frac{x}{3} \right) = 6 \times 5
$$

**Step 2: Simplify the Equation**

$$
3x + 2x = 30
$$

**Step 3: Combine Like Terms**

$$
5x = 30
$$

**Step 4: Solve for $$ x $$**

$$
x = \frac{30}{5} = 6
$$

**Answer:**

$$ x = 6 $$
$$ x = 6 $$

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