1. **State the problem:** Solve the linear equation $3x + 6 = 2x - 7$ for $x$. 2. **Formula and rules:** To solve for $x$, we use the properties of equality: we can add, subtract, multiply, or divide both sides of the equation by the same number without changing the equality. 3. **Step 1:** Subtract $2x$ from both sides to get all $x$ terms on one side: $$3x + 6 - 2x = 2x - 7 - 2x$$ which simplifies to $$x + 6 = -7$$ 4. **Step 2:** Subtract 6 from both sides to isolate $x$: $$x + 6 - 6 = -7 - 6$$ which simplifies to $$x = -13$$ 5. **Final answer:** The solution to the equation is $x = -13$. This means when $x$ is $-13$, both sides of the original equation are equal.