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by candygal79 » Fri Apr 04, 2014 12:32 am
Which of the following inequalities has a solution set that, when graphed on the number line, is a single segment of finite length ?

A x4 greater or equal 1

B x3 lesser or equal 27

C x2 greater or equal 16

D 2 lesser or equal|x|lesser or equal 5

E 2 lesser or equal 3x + 4 lesser or equal 6
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by [email protected] » Fri Apr 04, 2014 12:44 pm
Hi candygal79,

The equations in this question can be physically drawn or handled as a Number Property concept:

Note that the question asks for a SINGLE SEGMENT of FINITE LENGTH. This means that the group of numbers that make up the solution set would be consecutive and limited (as opposed to non-consecutive and/or infinite).

Here are the Number Properties:

A: X^4 >= 1

X can be 1, 2, 3, etc. or -1, -2, -3, etc. This group of answers is infinite and non-consecutive. Eliminate A.

B: X^3 <= 27

X can be 3, 2, 1, 0, -1, etc. This group is infinite. Eliminate B.

C: X^2 >= 16

X can be 4, 5, 6, etc. or -4, -5, -6, etc. This group is infinite and non-consecutive. Eliminate C.

D: 2 <= |X| <= 5

X can be 2, 3, 4, 5 or -2, -3, -4, -5, This group is finite BUT non-consecutive. Eliminate D.

E: 2 <= 3X + 4 <= 6

Let's simplify with algebra...

-2 <= 3X <= 2

-2/3 <= X <= 2/3

X is a finite set of answers and the answers are consecutive. This is a MATCH to what we're looking for.

Final Answer: E

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