Question: Solve #6-7 by clearing denominators
$\frac{x+4}{6} - \frac{3x}{2} = 5$
top-right: handwritten notes “+”, “x”, “-7”, “= 13” with a bracket-like mark near them
1. **State the problem:** Solve the equation $$\frac{x+4}{6} - \frac{3x}{2} = 5$$ by clearing denominators.
2. **Identify the denominators:** The denominators are $6$ and $2$.
3. **Find the least common denominator (LCD):** The LCD of $6$ and $2$ is $6$.
4. **Multiply both sides of the equation by the LCD to clear denominators:**
$$6 \times \left(\frac{x+4}{6} - \frac{3x}{2}\right) = 6 \times 5$$
5. **Distribute the $6$ inside the parentheses:**
$$6 \times \frac{x+4}{6} - 6 \times \frac{3x}{2} = 30$$
6. **Simplify each term:**
$$\cancel{6} \times \frac{x+4}{\cancel{6}} - 3 \times 3x = 30$$
which simplifies to
$$x + 4 - 9x = 30$$
7. **Combine like terms:**
$$x - 9x + 4 = 30$$
$$-8x + 4 = 30$$
8. **Isolate the variable term:**
$$-8x = 30 - 4$$
$$-8x = 26$$
9. **Solve for $x$ by dividing both sides by $-8$:**
$$x = \frac{26}{-8}$$
$$x = -\frac{13}{4}$$
**Final answer:** $$x = -\frac{13}{4}$$