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Re: ­Which of the following inequalities is equivalent to -9 <= x <= 3? [#permalink]
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Bunuel wrote:
­Which of the following inequalities is equivalent to \(-9 \leq x \leq 3\)?

A. \(x^2 \leq 9\)
B. \(|x-3| \leq 6\)
C. \(|x+3| \leq 6\)
D. \(|x+6| \leq 3\)
E. \(3 \leq |x| \leq 6\)­

 

­
A. \(x^2 \leq 9\)

\(-3 \leq x \leq 3\)

B. \(|x-3| \leq 6\)

\(-6 \leq x - 3 \leq 6\)

\(-3 \leq x \leq 9\)

C. \(|x+3| \leq 6\)

\(-6 \leq x + 3 \leq 6\)

\(-9 \leq x \leq 3\)

Option C­
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Re: ­Which of the following inequalities is equivalent to -9 <= x <= 3? [#permalink]
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­Given - "-9 <= x <= 3"

if you observe carefully you will notice the standard pattern of inequality with modulus.
Add +3 on each side of inequality 

-9+3 <= x+3 <= 3+3

-6 <= x+3 <= 6


This is standard pattern of |x+3| <= 6

Hence C.
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Re: ­Which of the following inequalities is equivalent to -9 <= x <= 3? [#permalink]
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­Which of the following inequalities is equivalent to \(-9 \leq x \leq 3\)?

Find the midpoint of the two extremes, \(-9\) and \(3\), which is \(\frac{-9 + 3}{2} = -3\).

Find the positive difference between each of the two extremes and the midpoint, which is \(3 - (-3) = 6\).

So, \(|x - (-3)| \leq 6\).

A. \(x^2 \leq 9\)
B. \(|x-3| \leq 6\)
C. \(|x+3| \leq 6\)
D. \(|x+6| \leq 3\)
E. \(3 \leq |x| \leq 6\)­

Correct answer: C­
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Re: ­Which of the following inequalities is equivalent to -9 <= x <= 3? [#permalink]
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