1. Given the problem: Solve for $x$ in the equation $2x + 3 = 7$. 2. Use the formula for solving linear equations: isolate $x$ by performing inverse operations. 3. Subtract 3 from both sides: $$2x + 3 - 3 = 7 - 3$$ $$2x = 4$$ 4. Divide both sides by 2: $$\frac{\cancel{2}x}{\cancel{2}} = \frac{4}{2}$$ $$x = 2$$ 5. Final answer: $$x = 2$$