Question: 3(x-4)+5=2x+12
1. **State the problem:** Solve the equation $$3(x-4)+5=2x+12$$ for $x$.
2. **Apply the distributive property:** Multiply $3$ by each term inside the parentheses.
$$3 \times x = 3x$$
$$3 \times (-4) = -12$$
So the equation becomes:
$$3x - 12 + 5 = 2x + 12$$
3. **Combine like terms on the left side:**
$$-12 + 5 = -7$$
So the equation is:
$$3x - 7 = 2x + 12$$
4. **Isolate variable terms on one side:** Subtract $2x$ from both sides.
$$3x - 7 - 2x = 2x + 12 - 2x$$
$$\cancel{3x} - 7 - \cancel{2x} = \cancel{2x} + 12 - \cancel{2x}$$
$$x - 7 = 12$$
5. **Isolate $x$ by adding $7$ to both sides:**
$$x - 7 + 7 = 12 + 7$$
$$x = 19$$
6. **Final answer:**
$$\boxed{19}$$