1. Let's consider the problem: Solve the equation $$2x + 3 = 11$$ for $x$. 2. The formula to solve a linear equation like this is to isolate $x$ by performing inverse operations. 3. First, subtract 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. So, the solution to the equation is $x = 4$. This example shows how to isolate the variable step-by-step by undoing addition and multiplication.