1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. We use the basic algebraic principle that to isolate $x$, we perform inverse operations to both sides of the equation. 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 $x$: $$\frac{2x}{\cancel{2}} = \frac{8}{\cancel{2}}$$ which simplifies to $$x = 4$$ 5. Therefore, the solution to the equation is $x = 4$.