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Maths-

General

Easy

Question

Solve absolute value equation :
$vertical line x vertical line minus 4 equals 9$

The correct answer is: x = 13, -13

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
$vertical line x vertical line equals open curly brackets table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell negative x comma x less than 0 end cell row cell x comma x greater or equal than 0 end cell end table close$
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
|x| - 4 = 9
Adding 4 from both sides, we get
|x| = 4+9
Simplifying the above equation, we can write
|x| = 13
Using the definition of absolute value,
$vertical line x vertical line equals open curly brackets table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell negative x comma x less than 0 end cell row cell x comma x greater or equal than 0 end cell end table close$
We get two possibilities,
For x < 0,
|x| = -x = 13
Thus, we get
x = -13
For x ≥ 0,
|x| = x = 13
We have
x = 13
Hence, we get two values of x satisfying the given equation,
x = 13, -13
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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