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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If 9 - x^2 ≥ 0, which of the following describes all

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Manager  Joined: 11 Aug 2012
Posts: 107
Schools: HBS '16, Stanford '16
If 9 - x^2 ≥ 0, which of the following describes all  [#permalink]

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3 00:00

Difficulty:   5% (low)

Question Stats: 83% (01:04) correct 18% (01:20) wrong based on 160 sessions

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If $$9 - x^2 \geq{} 0$$, 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"?
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Re: If 9 - x^2 ≥ 0, which of the following describes all  [#permalink]

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$$9 - x^2 \geq{} 0$$
$$- x^2 \geq{} -9$$
$$x^2 \leq{} 9$$

$$-3\leq{x}\leq{3}$$

danzig wrote:
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"?

Here we take the internal values between -3 and 3. I am not sure of what you mean in your question
Check this post tips-and-tricks-inequalities-150873.html

Let me know if it remains unclear
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Re: If 9 - x^2 ≥ 0, which of the following describes all  [#permalink]

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1
Please refer to the graph attached. ** Apologies for the sloppy paint work

As you can see, f(x) = x^2 - 9 = (x-3)(x+3) <=0 ***After changing sign multiply minus both sides. The only region possible would be the region between the roots of f(x) = 0 i.e.{-3,3}. Once can also go about and plot the inverted parabola for 9 - x^2 and prove the region is greater than 0 as well Hope it clears your doubts! Regards,
Arpan
Attachments graph-fun.png [ 9.17 KiB | Viewed 2833 times ]

Math Expert V
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Posts: 65014
Re: If 9 - x^2 ≥ 0, which of the following describes all  [#permalink]

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danzig wrote:
If $$9 - x^2 \geq{} 0$$, 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"?

Check here: if-x-is-an-integer-what-is-the-value-of-x-1-x-2-4x-94661.html#p731476

Hope it helps.
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Joined: 23 Feb 2015
Posts: 1938
Re: If 9 - x^2 ≥ 0, which of the following describes all  [#permalink]

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danzig wrote:
If $$9 - x^2 \geq{} 0$$, 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

$$9 - x^2 \geq{} 0$$
=>9≥x^2
=> root 9≥root x^2
=> 3≥absolute value of x
absolute value of x≤3
so, if x positive, then x≤3
but, if x negative, then
-x≤3
=>x≥-3
if we combined the values of x then it will be...
3 ≥ x ≥ -3
The correct choice is A.
Thank you...
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Target Test Prep Representative G
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Joined: 04 Mar 2011
Posts: 2799
Re: If 9 - x^2 ≥ 0, which of the following describes all  [#permalink]

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danzig wrote:
If $$9 - x^2 \geq{} 0$$, 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

Let’s solve the given inequality:

9 - x^2 ≥ 0

9 > x^2

√9 ≥ √x^2

3 ≥ |x|

Thus: 3 ≥ x

or

3 ≥ -x

-3 ≤ x

Finally, we can say: -3 ≤ x ≤ 3.

_________________

# Jeffrey Miller

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Re: If 9 - x^2 ≥ 0, which of the following describes all  [#permalink]

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_________________ Re: If 9 - x^2 ≥ 0, which of the following describes all   [#permalink] 02 Jun 2020, 21:41

# If 9 - x^2 ≥ 0, which of the following describes all  