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Re: If x^2 +4x -32 <0, which of the following must be true [#permalink]
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Raxit85 wrote:
If x^2 +4x -32 <0, which of the following must be true?

1. |x+2|<6
2. -8 < x < 4
3. |x+7| < 2

A) I Only
B) II Only
C) III only
D) I and II only
E) I, II, and III


Solution:

Since two of the three statements have absolute values, we should solve the inequality by completing the square:

x^2 + 4x - 32 < 0

x^2 + 4x < 32

x^2 + 4x + 4 < 32 + 4

(x + 2)^2 < 36

Now, taking the square root of both sides (recall that √(X^2) = X), we have

|x + 2| < 6

We see that statement 1 is true. Solving this further (recall that |X| < k where k is a positive number means -k < X < k) , we have:

-6 < x + 2 < 6

-8 < x < 4

So statement 2 is true also. However, statement 3 will not be true since it’s a different statement from statement 1.

Answer: D
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Re: If x^2 +4x -32 <0, which of the following must be true [#permalink]
Hi,

Will it be easire for these kind of questions to directly use numbers or do them algerbically?
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Re: If x^2 +4x -32 <0, which of the following must be true [#permalink]
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Re: If x^2 +4x -32 <0, which of the following must be true [#permalink]
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