Given:

< 2, x ϵ R.

-2 < < 2

> -2 and < 2

When,

> -2

Adding 2 to both sides in the above equation

+ 2 > -2 + 2

> 0

> 0

> 0

Signs of 4x – 3:

4x – 3 = 0 →

(Adding 3 to both sides and then dividing both sides by 4)

4x – 3 > 0 →

(Adding 3 to both sides and then dividing both sides by 4)

4x – 3 < 0 →

(Adding 3 to both sides and then dividing both sides by 4)

Signs of x – 1:

x – 1 = 0 → x = 1 (Adding 1 to both the sides)

x – 1 > 0 → x > 1 (Adding 1 to both the sides)

x – 1 < 0 → x < 1 (Adding 1 to both the sides)

At x = 1, is not defined.

Intervals that satisfy the required condition: > 0

or x > 1

Now, when < 2

Subtracting 2 from both the sides

-2 < 2 -2

< 0

< 0

< 0

Signs of x – 1:

x – 1 = 0 → x = 1 (Adding 1 on both the sides)

x – 1 < 0 → x < 1 (Adding 1 on both the sides)

x – 1 > 0 → x > 1 (Adding 1 on both the sides)

At x = 1, is not defined

Interval which satisfy the required condition: < 0

x < 1

Now, combining the intervals:

or x > 1 and x <1

Merging the overlapping intervals:

Therefore,