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# ­Which of the following inequalities is equivalent to -9 <= x <= 3?

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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]
­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. $$3 \leq |x| \leq 6$$­