The correct answer is: x = -7, -3

Step by step solution:
The given equation is
2|x + 5| = 4
Using the definition of absolute value,

We get two possibilities,
For x + 5 < 0,
2|x + 5| = -2(x + 5) = 4
Simplifying, we get
-2x - 10 = 4
Adding 10 both sides, we have
-2x = 4 + 10 = 14
Dividing throughout by -2, we get
x = -7
For x + 5 ≥ 0,
2|x + 5| = 2(x + 5) = 4
Simplifying, we get
2x + 10 = 4
Subtracting 10 both sides, we get
2x = 4 - 10 = -6
Dividing by 2 throughout, we get
x = -3
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’.