Question

# What is the value of x in

## The correct answer is: x = -5, -7

### Step by step solution:

The given equation is

3|x + 6| + 8 = 5

Using the definition of absolute value,

We get two possibilities,

For x + 6 < 0,

3|x + 6| + 8 = 3{-(x + 6)} + 8 = 5

Simplifying, we get

-3(x + 6) + 8 = 5

Subtracting 8 both sides and simplifying the left hand side, we have

-3x - 18 = 5 - 8= -3

Adding 18 on both sides, we get

- 3x = -3 + 18 = 15

Dividing throughout by -3, we get

x = -5

For x + 6 ≥ 0,

3|x + 6| + 8 = 3(x + 6) + 8 = 5

Simplifying the left hand side, we get

3x + 18 + 8 = 5

⇒3x + 26 = 5

Subtracting 26 both sides, we get

3x = 5 - 26 = -21

Dividing by 3 throughout, we get

x = -7

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

x = -5, -7

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’.

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