Question

# Solve absolute value equation :

Hint:

### |x| is known as the absolute value of x. It is the non-negative value of x irrespective of its sign. The value of absolute value of x is given by

First, we simplify the equation. We will get two cases in the solution of the given equation. We apply the given definition and then simplify the two equations to get the value of x.

## The correct answer is: Hence, we get two values of x satisfying the given equation, x=7, -3

Step by step solution:

The given equation is

3 |x-2| - 8 = 7

Adding 8 both sides, we get

3 |x-2| = 7+ 8 = 15

Dividing by 3 throughout, we get

|x-2| = 5

Using the definition of absolute value,

We get two possibilities,

For x - 2 < 0,

|x-2| = - (x-2) = 5

Simplifying, we get

- x + 2 = 5

Subtracting 2 from both sides, we have

- x = 5 - 2 = 3

Dividing throughout by -1, we get

x = - 3

For - 2≥0,

|x-2| = x - 2 = 5

Adding 2 both sides, we get

x = 5 + 2 = 7

Hence, we get two values of x satisfying the given equation,

x = 7, - 3

Adding 8 both sides, we get

Dividing by 3 throughout, we get

Using the definition of absolute value,

We get two possibilities,

Simplifying, we get

Subtracting 2 from both sides, we have

Dividing throughout by -1, we get

Adding 2 both sides, we get

Hence, we get two values of x satisfying the given equation,

Absolute value of a variable has many uses in mathematics. Geometrically, the absolute value of a number may be considered as its distance from zero regardless of its direction. The symbol |.| is pronounced as ‘modulus’. We read |x| as ‘modulus of x’ or ‘mod x’.