Question

Solve the given inequality for real x: 3x-7 > 5x-1

Answer 1

3x – 7 > 5x – 1
⇒ 3x – 7 + 7 > 5x – 1 + 7
⇒ 3x > 5x + 6
⇒ 3x – 5x > 5x + 6 – 5x
⇒ – 2x > 6
⇒ $\frac {-2x}{-2}$ < $\frac {6}{-2}$
⇒ x < -3
Thus, all real numbers x, which are less than –3, are the solutions of the given inequality.
Hence, the solution set of the given inequality is (–∞, –3).