If 9 - x2 ≥ 0

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 142
Joined: Sun Jun 12, 2011 7:55 am
Thanked: 5 times
Followed by:3 members

If 9 - x2 ≥ 0

by metallicafan » Tue May 21, 2013 8:55 am
If 9 - x2 ≥ 0 , which of the following describes all possible values of x ?

A. 3 ≥ x ≥ -3

B. x ≥ 3 or x ≤ -3

C. 3 ≥ x ≥ 0

D. -3 ≥ x

E. 3 ≤ x

My doubt is this:
When we solve the inequality, we get this:

x ≤ 3 ; x ≥ -3

Is x ≤ 3 AND x ≥ -3?, or
x ≤ 3 OR x ≥ -3?

In other words, should we find the intersection between those values? (In that case, it would be "AND"?

But what about if we had gotten this: x ≤ - 3 ; x ≥ 3 ? What would the answer be? x ≤ - 3 OR x ≥ 3?, or "there are no values for x"?
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Tue May 21, 2013 9:17 am
metallicafan wrote:If 9 - x2 ≥ 0 , which of the following describes all possible values of x ?

A. 3 ≥ x ≥ -3

B. x ≥ 3 or x ≤ -3

C. 3 ≥ x ≥ 0

D. -3 ≥ x

E. 3 ≤ x
NOTE: I'm assuming that you meant to write 9 - x^2 > 0

Given: 9 - x^2 > 0
Add x^2 to both sides: 9 > x^2
At this point we may see that it must be true that -3 < x < 3
Answer = A

Alternatively, once we know that 9 > x^2 we can find some values for x that satisfy this inequality.
For example, if 9 > x^2, then x = -2 is one possible value for x.
Now check the answer choices to see which one(s) allows for x to equal -2

Only answer choice A allows for the possibility that x = -2

So, the correct answer must be A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image