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21 May 2013, 09:46
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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
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"?
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"?
21 May 2013, 09:51
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\(9 - x^2 \geq{} 0\)
\(- x^2 \geq{} -9\)
\(x^2 \leq{} 9\)
\(-3\leq{x}\leq{3}\)
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
\(- x^2 \geq{} -9\)
\(x^2 \leq{} 9\)
\(-3\leq{x}\leq{3}\)
danzig
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
arpanpatnaik
GMAT 1: 640 Q42 V37
Posts: 101
21 May 2013, 09:57
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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
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
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