1. The problem is to solve the equation $2x + 3 = 7$ for $x$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations. 3. First, subtract 3 from both sides to get rid of the constant term on the left: $$2x + 3 - 3 = 7 - 3$$ 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 $$x = 2$$ 5. Therefore, the solution to the equation is $x = 2$. This means when $x$ is 2, the original equation holds true.