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

⇒ `(-2x)/-2 < 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).