Question

What is the solution if any, to the inequality 3-l4-nl>1?

Answer 1

Answer:

The solution to the inequality is all real values of n that respect the following condition: 2 < n < 6

Step-by-step explanation:

First, we need to separate the modulus from the rest of equation. So

3-l4-nl>1

-|4-n|>1-3

-|4-n|>-2

Multiplying everything by -1.

|4-n|<2

How to solve:

|x| < a means that -a<x<a

In this question:

|4-n|<2

-2<4-n<2

This means that:

4 - n > -2

-n > -6

Multiplying by -1

n < 6

And

4 - n < 2

-n < -2

Multiplying by 1

n > 2

Intersection:

Between n > 2 and n < 6 is 2 < n < 6

So the solution to the inequality is all real values of n that respect the following condition: 2 < n < 6