1. Let's start with a simple algebra problem suitable for grade 9 students: Solve for $x$ in the equation $2x + 3 = 11$. 2. The formula we use here is to isolate $x$ by performing inverse operations. Important rules: addition and subtraction undo each other, multiplication and division undo each other. 3. First, subtract 3 from both sides to get rid of the +3: $$2x + 3 - 3 = 11 - 3$$ which simplifies to $$2x = 8$$ 4. Next, divide both sides by 2 to solve for $x$: $$\frac{2x}{\cancel{2}} = \frac{8}{\cancel{2}}$$ which simplifies to $$x = 4$$ 5. So, the solution is $x = 4$. This means if you replace $x$ with 4 in the original equation, both sides will be equal. 6. To check, substitute $x=4$ back: $$2(4) + 3 = 8 + 3 = 11$$ which matches the right side. Therefore, $x=4$ is the correct answer.