Which are the following solutions to |5x-4| is greater than 16?

|5x-4| > 16

The  |5x-4| is the modulus of (5x - 4), so we will look at two cases where (5x - 4) is positive and negative.

Positive

(5x - 4) > 16

5x > 16 + 4

5x > 20

x > 20/5

x > 4

Negative case

-(5x - 4) > 16

Divide both sides by -1 and the sign reverses.

(5x - 4)  < 16/-1

5x - 4 < -16

5x < -16 + 4

5x < 4 - 16

5x < -12

x < -12/5

x < -2.4

So the solutions are x > 4 and x < -2.4

Combining both solutions:          -2.4 > x > 4

Hope this explains it.