1. **Stating the problem:** Solve the linear equation $8x + 9 = 4x + 12$ for $x$. 2. **Formula and rules:** To solve linear equations, we isolate the variable $x$ by performing the same operations on both sides of the equation. 3. **Step-by-step solution:** - Start with the equation: $$8x + 9 = 4x + 12$$ - Subtract $4x$ from both sides to get all $x$ terms on one side: $$8x - 4x + 9 = 12$$ - Simplify: $$4x + 9 = 12$$ - Subtract 9 from both sides to isolate the $x$ term: $$4x = 12 - 9$$ - Simplify the right side: $$4x = 3$$ - Divide both sides by 4 to solve for $x$: $$x = \frac{3}{4}$$ 4. **Answer:** The solution to the equation is $x = \frac{3}{4}$.