Which of the following expressions is equal to 0 for some value of x?
|x - 1| - 1
|x + 1| + 1
|1 - x| + 1
|x - 1| + 1

Solution:

We have to find the expression which is equal to 0 for some value of x.

We know that |a| of any number is non negative.

This implies |a| is always positive.

Considering |x - 1| - 1

Let x = 2

|x - 1| - 1 = |2 - 1| - 1

= |1| - 1

= 1 - 1

= 0

Considering |x + 1| + 1

Let x = -2

|x + 1| + 1 = |-2 + 1| + 1

= |-1| + 1

= 1 + 1

= 2

Considering |1 - x| + 1

Let x = 2

|1 - x| + 1 = | 1 - 2| + 1

= |-1| + 1

= 1 + 1

= 2

Considering |x - 1| + 1

Let x = 2

|x - 1| + 1 = |2 - 1| + 1

= |1| + 1

= 1 + 1

Therefore, the expression |x - 1| - 1 is equal to 0 for some value of x.

---

Which of the following expressions is equal to 0 for some value of x?

Summary:

The expression |x - 1| - 1 is equal to 0 for some value of x.