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Which of the following describes all values of x for which

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by BTGmoderatorDC » Mon Apr 29, 2019 8:30 pm

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Answers

A

B

C

D

E

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Difficulty—

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

OA E

Source: Official Guide
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by Jay@ManhattanReview » Mon Apr 29, 2019 9:11 pm
BTGmoderatorDC 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

OA E

Source: Official Guide
We are given that 1 - x^2 ≥ 0 => 1 ≥ x^2. This implies that the absolute value of x must not exceed 1. Thus, we have -1 ≤ x ≤ 1.

The correct answer: E

Hope this helps!

-Jay
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by Scott@TargetTestPrep » Mon May 06, 2019 7:04 pm
BTGmoderatorDC 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

OA E

Source: Official Guide
Simplifying, we have:

1 ≥ x^2

√1 ≥ √x^2

1 ≥ |x|

Now we solve for x:

When x is positive:

1 ≥ |x|

1 ≥ x

x ≤ 1

This can be re-expressed as x ≤ 1.

When x is negative:

1 ≥ |x|

1 ≥ -x

-1 ≤ x

We combine the two resulting inequalities to get:

-1 ≤ x ≤ 1

Answer: E

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