Question: Solve the following equation for x. Express your answer in the simplest form.
3(-4x + 7) = 24x - 32
1. **State the problem:** Solve the equation $$3(-4x + 7) = 24x - 32$$ for $$x$$.
2. **Apply the distributive property:** Multiply $$3$$ by each term inside the parentheses.
$$3 \times (-4x) + 3 \times 7 = 24x - 32$$
which simplifies to
$$-12x + 21 = 24x - 32$$
3. **Collect like terms:** Add $$12x$$ to both sides to get all $$x$$ terms on one side.
$$-12x + 21 + 12x = 24x - 32 + 12x$$
which simplifies to
$$21 = 36x - 32$$
4. **Isolate the $$x$$ term:** Add $$32$$ to both sides.
$$21 + 32 = 36x - 32 + 32$$
which simplifies to
$$53 = 36x$$
5. **Solve for $$x$$:** Divide both sides by $$36$$.
$$\frac{53}{\cancel{36}} = x \times \frac{\cancel{36}}{36}$$
which simplifies to
$$x = \frac{53}{36}$$
6. **Final answer:** $$x = \frac{53}{36}$$, which is already in simplest form.