in-equality

[Gary Wessle]

Hi

I am confused as to the steps of finding the value of x in the 2
different in-equalities below.

x^2 >= 9

and

x^2 <= 9
****************************************************************
the first

x^2 >= 9
I am not sure how to start, should I go
x >= +/- 3
and if not, then why, I need math proves step-by-step.

thanks

[WONG Wai-chi, Norme]

You may try this, though may seem unnecessary for Maths talents.

For example,
x^2 >=9
x^2 - 9 >= 0
(x + 3)(x - 3) >= 0
Using table to list out:
x <-3 =-3 -3<x<3 =3 >
3
(x+3)(x-3) + 0 -
0 +

so, the solution is x<=-3 or x>=3

By the same way,
x^2 <=9
(x+3)(x-3) <=9

so, the solution is -3 <= x <= 3



Gary Wessle ¼g¹D¡G

Post by Gary Wessle
Hi
I am confused as to the steps of finding the value of x in the 2
different in-equalities below.
x^2 >= 9
and
x^2 <= 9
****************************************************************
the first
x^2 >= 9
I am not sure how to start, should I go
x >= +/- 3
and if not, then why, I need math proves step-by-step.
thanks

[Barry Schwarz]

Post by Gary Wessle
Hi
I am confused as to the steps of finding the value of x in the 2
different in-equalities below.
x^2 >= 9
and
x^2 <= 9
****************************************************************
the first
x^2 >= 9
I am not sure how to start, should I go
x >= +/- 3
and if not, then why, I need math proves step-by-step.

x >= -3 introduces a set of values (e.g., -2) for which the condition
does not hold.

What you need to say is
x >= 3 OR x <= -3

You should be able to do the rest.