Solve the given inequality for real x: 4x + 3 < 5x + 7
4x + 3 < 5x + 7 ⇒ 4x + 3 – 7 < 5x + 7 – 7 ⇒ 4x – 4 < 5x ⇒ 4x – 4 – 4x < 5x – 4x ⇒ –4 < x
Thus, all real numbers x, which are greater than –4, are the solutions of the given inequality. Hence, the solution set of the given inequality is (–4, ∞).
