Maths-
General
Easy
Question
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
So, 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: 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’.
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