Solve absolute value equation :

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

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’.