1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate the variable $x$ by performing inverse operations. Important rules: addition and subtraction are inverse operations, as are multiplication and division. 3. Start by subtracting 3 from both sides: $$2x + 3 - 3 = 11 - 3$$ which simplifies to $$2x = 8$$ 4. Next, divide both sides by 2 to solve for $x$: $$\frac{\cancel{2}x}{\cancel{2}} = \frac{8}{2}$$ which simplifies to $$x = 4$$ 5. Therefore, the solution to the equation is $x = 4$.