Maths-
General
Easy
Question
Solve each absolute value equation :
The correct answer is: x = -4, 12
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 simplify the equation as much as possible and then apply the above definition to get the value of x.
Step by step solution:
The given equation is
|2x - 8 |= 16
Using the definition of absolute value,
We get two possibilities,
For 2x - 8 < 0,
|2x - 8| = -(2x - 8) = 16
Simplifying, we get
-2x + 8 = 16
Subtracting 8 both sides, we have
-2x = 16 - 8 = 8
Dividing throughout by -2, we get
x = -4
For 2x - 8 ≥ 0,
|2x - 8| = 2x - 8 = 16
Adding 8 both sides, we get
2x = 16 + 8 = 24
Dividing by 2 throughout, we get
x = 12
Hence, we get two values of x satisfying the given equation,
x = -4, 12
Note:
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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