Answer:
n > 2 or n < 6
Step-by-step explanation:
3 - | 4 - n | < 1
Let's move 3 to the other side of the equation:
- | 4 - n | < 1 - 3
- | 4 - n | < -2
Both sides of the equation are negative, so we can simplify by multiplying them with -1:
(- | 4 - n | < -2*-1
| 4 - n | < 2
We cannot get rid of the module because it's not for a single number and we dont know what n is equal to but there is a rule that we can use to remove the module:
- if | x | < a and a > 0 then -a < x < a. So if we use it we get the following:
- 2 < 4 - n < 2
These are two equations, separate and solve them separately
4 - n < 2
- n < 2 - 4
- n < -2
n > 2 (< turns into > because we changed sign)
and
- 2 < 4 - n
4 - n > -2
-n > -2 - 4
n < 6 (we change the sign of the numbers so the equation changes too)
So after solving the two equation we get the answers
