Question: User: 3(x − 1) = 2x + 9
1. **State the problem:** Solve the equation $$3(x - 1) = 2x + 9$$ for $$x$$.
2. **Apply the distributive property:** Multiply $$3$$ by each term inside the parentheses.
$$3(x - 1) = 3 \times x - 3 \times 1 = 3x - 3$$
So the equation becomes:
$$3x - 3 = 2x + 9$$
3. **Isolate the variable terms on one side:** Subtract $$2x$$ from both sides.
$$3x - 3 - 2x = 2x + 9 - 2x$$
$$\cancel{3x} - 3 - \cancel{2x} = \cancel{2x} + 9 - \cancel{2x}$$
Simplifies to:
$$x - 3 = 9$$
4. **Isolate $$x$$:** Add $$3$$ to both sides.
$$x - 3 + 3 = 9 + 3$$
$$x + \cancel{-3} + \cancel{3} = 12$$
$$x = 12$$
5. **Final answer:** $$x = 12$$