1. The problem is to solve the equation $2x + 3 = 7$ for $x$. 2. We use the basic algebraic principle: to isolate $x$, perform inverse operations on both sides of the equation. 3. First, subtract 3 from both sides: $$2x + 3 - 3 = 7 - 3$$ which simplifies to $$2x = 4$$ 4. Next, divide both sides by 2 to solve for $x$: $$\frac{2x}{2} = \frac{4}{2}$$ which simplifies to $$\cancel{2}x / \cancel{2} = 2$$ 5. Therefore, the solution is: $$x = 2$$ This means that when $x$ is 2, the original equation holds true.