Question: Solve the equation.
5(2x + 6) - 3(4x - 3) = 9
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The solution to the equation is x = □.
1. **State the problem:** Solve the equation $$5(2x + 6) - 3(4x - 3) = 9$$.
2. **Apply the distributive property:**
$$5 \times 2x + 5 \times 6 - 3 \times 4x + 3 \times 3 = 9$$
which simplifies to
$$10x + 30 - 12x + 9 = 9$$.
3. **Combine like terms:**
$$10x - 12x + 30 + 9 = 9$$
$$-2x + 39 = 9$$.
4. **Isolate the variable term:**
Subtract 39 from both sides:
$$-2x + 39 - 39 = 9 - 39$$
$$-2x = -30$$.
5. **Solve for $$x$$ by dividing both sides by $$-2$$:**
$$x = \frac{-30}{-2}$$
Use cancellation to simplify:
$$x = \frac{\cancel{-30}}{\cancel{-2}} \times \frac{-1}{-1} = 15$$.
6. **Final answer:**
$$x = 15$$.