Question

how is this possible?

Answer 1

Q : If
${x}^{2} - 4 \geqslant 0 \\ = > x \geqslant 2 \: \: \: \: or \: x \: \leqslant - 2 \: \: (reason)$

This is just example, so for general proof see pic.
As Maths requires more general explanation of concepts with examples.
First see example then proof
Ans.
Let x = 5 which satisfies x >=2 ,
=> It should also satisfy x^2 - 4>=0

Proof:
LHS = x^2 - 4
= 5^2 - 4
= 21 >=0 .
Yes, x = 5 is satisfied.

Let x = -5 which satisfy x<=-2.
then it should also satisfy
x^2 - 4 >=0

Proof:
x^2 - 4 = (-5)^2 -4
=25 -4 = 21 >=0
Yes, it also satisfies.

We also. see that x = 2 , satisfies.

But -2<x < 2.,
does not satisfy this.
Proof :
Let x = 1 ,
we get
x^2 - 4 =1^2 - 4 = -3 which is negative.
and
x > = 2 or x<= -2 also does not satisfy this as this 1 is between -2 and 2 .
For More General proof see pic.