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.