For how many integers x is the following true: /2-4x/<14

For how many integers x is the following true: /2-4x/<14
Please show your work! Thanx!!

|2 − 4x| < 14
This implies:
2 − 4x < 14 AND 2 − 4x > -14
-4x < 12
x > -3

-4x > -16
x < 4

Therefore:
x > -3 AND x < 4
Which can be combined and written as:
-3 < x < 4
Or, in interval notation:
(-3, 4)

Therefore, this is true for all the numbers in between, but not including -3 and 4, so:
4 − (-3) − 1
= 4 + 3 − 1
= 6 integers.

Since we have absolute values, we are going to have two versions: a positive and a negative version.

|2-4x|<14

2-4x<14 or 2-4x>-14
-2 -2 -2 -2
-4x<12 -4x>-16
/-4 /-4 /-4 /-4
x>-3 x<4

It looks like this is going to work for all integers between -3 and 4.

Separate into two cases, one where 2-4x is greater than or equal to zero and one where 2-4x is less than zero.