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

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29 Sep 2015, 19:39

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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.

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

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04 Nov 2016, 18:58

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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

In such inequalities, as long as one can factorize the expression into linear factors, the most methodical way to approach such questions is to use the wavy line approach.

You can refer to the following posts for a comprehensive treatment of the Wavy Line Approach:

Mark the zero points on the number and draw the wavy line. Identify the \(+ve\) and \(-ve\) regions of the curve. Since we need the range of values of \(x\), for which the expression in (1) is less than or equal to zero, we consider the \(-ve\) region(s) along with the zero points.

Working Out:

The range of values of \(x\) for which the given inequality is satisfied is \(-1 \leq x \leq 1\)

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