Solve the inequalities in Exercises 5 to 16 for real x:

3x – 7 > 5x – 1

It is given in the question that,

3x – 7 > 5x – 1

Adding 7 to both the sides,

3x – 7 + 7 > 5x – 1 + 7

3x> 5x + 6

Subtracting 5x from both the sides,

3x – 5x > 5x + 6 – 5x

-2x > 6

Dividing both sides by -2

x < -3

∴ The solutions of the given inequality are defined by all the real numbers less than -3.

Thus, (-∞, -3) is the required solution set.