Solve 2x + 3 = 11. Explain why each step is valid.

To isolate the term $2x$, we need to eliminate the constant term $+3$ from the left side of the equation. We do this by subtracting 3 from both sides of the equation. This is valid due to the Subtraction Property of Equality, which states that if you subtract the same quantity from both sides of an equation, the equality remains true.

$$2x + 3 - 3 = 11 - 3$$ $$2x = 8$$

Now that we have $2x = 8$, we need to isolate $x$. Since $x$ is being multiplied by 2, we perform the inverse operation, which is division. We divide both sides of the equation by 2. This is valid due to the Division Property of Equality, which states that if you divide both sides of an equation by the same non-zero quantity, the equality remains true.

$$\frac{2x}{2} = \frac{8}{2}$$ $$x = 4$$