corvinis wrote:

If |x| > 3, which of the following must be true?

I. x > 3

II. x^2 > 9

III. |x - 1| > 2

A. I only

B. II only

C. I and II only

D. II and III only

E. I, II, and III

If |x| > 3, then it must be true that

EITHER x > 3 OR x < -3(1) x > 3This need not be true, since it's also possible that x < -3.

For example, x COULD equal -5

So, statement I need not be true.

ELIMINATE answer choice A, C and E

(2) x² > 9This means that EITHER x > 3 OR x < -3

Perfect - this matches our original conclusion that

EITHER x > 3 OR x < -3(3) |x-1| > 2Let's solve this further.

We get two cases:

case a) x - 1 > 2, which means x > 3 PERFECT

or

case b) x - 1 < -2, which means x < -1

Must it be true that x < -1?

YES.

We already learned that

EITHER x > 3 OR x < -3If

x < -3, then we can be certain that x < -1

For example, if I tell you that the temperature is less than -3 degrees Celsius, can we be certain that the temperature is less than -1 degrees? Yes.

So, statement 3 must also be true.

Answer: D

Cheers,

Brent

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