Solve for x: |x − 2| + 10 = 12

A modulus function gives the magnitude of a number irrespective of its sign. It is also called the absolute value function.

Answer: x = 0 and x = 4 are the roots for x: |x − 2| + 10 = 12

The modulus function always gives a non-negative value of any number or variable.

Explanation:

Let us try to solve the expression for both the positive and negative values of (x-2)

So, if x - 2 > 0, x is positive

|x − 2| + 10 = 12

⇒ x - 2 + 10 = 12

⇒ x + 8 = 12

⇒ x = 12 - 8

⇒ x = 4

And if x - 2 < 0, x is negative

|x − 2| + 10 = 12

⇒ 2 - x + 10 = 12 

⇒ 12- x = 12

⇒ x = 12 - 12

⇒ x = 0

Hence x = 0 and x =4 are the roots for x: |x − 2| + 10 = 12