selim wrote:

If x is an integer such that 5 < x < 11, 7 < x < 13, and x + 2 < 12 how many integers will satisfy x?

A. 1

B. 2

C. 3

D. 4

E. none of these

We have the following:

For 5 < x < 11, we see that x could be 5, 6, 7, 8, 9, or 10.

For 7 < x < 13, we see that x could be 8, 9, 10, 11, or 12.

Thus, for the first two inequalities, x could be 8, 9, or 10.

We can simplify x + 2 < 12 as x < 10.

Thus, the only integers that satisfy all three inequalities are 8 and 9.

Answer: B

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Jeffery Miller

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