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Which of the following describes all values of x for which 1

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Which of the following describes all values of x for which 1 [#permalink]

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Which of the following describes all values of x for which 1–x^2 >= 0?

(A) x >= 1
(B) x <= –1
(C) 0 <= x <= 1
(D) x <= –1 or x >= 1
(E) –1 <= x <= 1
[Reveal] Spoiler: OA
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Re: Which of the following describes all values of x for which 1 [#permalink]

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Re: Which of the following describes all values of x for which 1 [#permalink]

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New post 27 May 2014, 02:57
Bunuel wrote:
Walkabout wrote:
Which of the following describes all values of x for which 1–x^2 >= 0?

(A) x >= 1
(B) x <= –1
(C) 0 <= x <= 1
(D) x <= –1 or x >= 1
(E) –1 <= x <= 1


\(1-x^2\geq{0}\) --> \(x^2\leq{1}\) --> \(-1\leq{x}\leq{1}\).

Answer: E.



Bunuel, Can you explain how we go from \(x^2\) to x in last step
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Re: Which of the following describes all values of x for which 1 [#permalink]

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New post 27 May 2014, 03:17
Which of the following describes all values of x for which 1–x^2 >= 0?

(A) x >= 1

Plugged in 2. 1–(2)^2 >= 0 -3>=0? NO. Wrong

(B) x <= –1

Plugged in -2. 1–(-2)^2 >= 0 -3>=0? NO. Wrong

(C) 0 <= x <= 1
Plugged in 0, 1, and 1/2. All of them work. But E is better because it describes all the values of x

(D) x <= –1 or x >= 1
A and B answer this. Wrong.

(E) –1 <= x <= 1

X is a positive or negative fraction or a zero.
x = -1/2 x = 1/2 x = 0
Plug all of them. They work.
Answer is E.

Another solution:
1–x^2 >= 0
1>= x^2
Therefore, -1=<x=<1
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Re: Which of the following describes all values of x for which 1 [#permalink]

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New post 27 May 2014, 03:37
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jatinsachani wrote:
Bunuel wrote:
Walkabout wrote:
Which of the following describes all values of x for which 1–x^2 >= 0?

(A) x >= 1
(B) x <= –1
(C) 0 <= x <= 1
(D) x <= –1 or x >= 1
(E) –1 <= x <= 1


\(1-x^2\geq{0}\) --> \(x^2\leq{1}\) --> \(-1\leq{x}\leq{1}\).

Answer: E.



Bunuel, Can you explain how we go from \(x^2\) to x in last step


Hello,

You have \(1-x^2\geq{0}\).
Since LHS and RHS are non-negative,we can take square root on both sides and get

\(1\geq{\sqrt{x^2}}\)

Also, \(\sqrt{x^2}\)=|x| so we have \(|x|\leq{1}\)
So x is between \(-1\leq{x}\leq{1}\)

Also, you can do it as \(1-x^2\geq{0}\) or \((1-x)(1+x)\geq{0}\) (using \(a^2-b^2=(a-b)(a+b)\) )

We need to find in which region does the equation hold true...try values of x <-1, -1<x<1 and x>1 to see where the relationship holds true

You need to brush your basics on mod values. Check out below links

graphic-approach-to-problems-with-inequalities-68037.html
math-number-theory-88376.html
if-x-is-an-integer-what-is-the-value-of-x-1-x-2-4x-94661.html#p731476
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Re: Which of the following describes all values of x for which 1 [#permalink]

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New post 26 Jun 2014, 16:16
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(1-x^2) >= 0 can be expressed as (1-x) (1+x) >=0

So 1-x>=0 (OR) 1+x>=0.

Therefore, 1 >= x (OR) x >= -1
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Re: Which of the following describes all values of x for which 1 [#permalink]

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Re: Which of the following describes all values of x for which 1 [#permalink]

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New post 30 Sep 2015, 11:13
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Hi All,

With inequality-based questions, sometimes the easiest approach is just to come up with a few examples that 'fit' the given prompt and then use those examples to eliminate answer choices.

Here, we're told that 1 - X^2 >= 0. We're asked for ALL of the possible values that fit this inequality.

The 'easiest' value that most Test Takers would immediately 'see' is 1 (since 1 - 1^2 = 0), so X COULD be 1.

Next, since we're dealing with a squared term, -1 would also be a solution (since 1 - [-1]^2 = 0).

So we immediately have at least two solutions: 1 and -1. We can eliminate Answers A, B and C.

For the last step, we have to determine what OTHER solutions are possible. You can either prove that fractions fit (try using X = 1/2) or proving that larger integers do NOT fit (try using X = 2). Either way, you can eliminate the final incorrect answer.

Final Answer:
[Reveal] Spoiler:
E


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Re: Which of the following describes all values of x for which 1   [#permalink] 30 Sep 2015, 11:13
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