1. Stating the problem: Solve the linear equation $2x + 3 = 11$ for $x$. 2. Formula and rules: To solve for $x$, isolate the variable by performing inverse operations. Subtract 3 from both sides, then divide both sides by 2. 3. Intermediate work: $$2x + 3 = 11$$ Subtract 3 from both sides: $$2x = 11 - 3$$ $$2x = 8$$ Divide both sides by 2: $$x = \frac{8}{2}$$ $$x = 4$$ 4. Explanation: We first remove the constant term on the left side by subtracting 3 from both sides. Then, since $x$ is multiplied by 2, we divide both sides by 2 to isolate $x$. The solution is $x=4$. Final answer: $x = 4$