2014-07-16 09:00:57

Which of the following integers is in the solution set of |2 - 5x| < 10

I. 2
II. -2
III. 2.3

(A) I only
(B) III only
(C) I and III only
(D) I, II, and III
(E) None of the above 

The correct answer is A
Explanation: When dealing with inequalities, set up two equations, since either the positive value of 2 - 5x is less than 10 or the negative value of it is less than 10:

2 - 5x < 10          or          -(2 - 5x) < 10

In the first equation, subtract 2 from both sides to get -5x < 8. Now, divide both sides by - 5, and remember to flip the inequality sign. This leaves x > -8/5, or -1.6.

In the second equation, start by dividing both sides by -1 to get rid of the negative sign. Remember to flip the inequality sign too. This leaves 2 - 5x > -10. Next, subtract 2 from both sides to get -5x > -12. Divide both sides by - 5, and flip the inequality sign again, leaving x < 12/5.

Thus, x is between -8/5 and 12/5, or -1.6 and 2.4: -1.6 < x < 2.4. Of the choices, 2 alone is in that range and an integer (2.3 is not an integer), making choice A correct.

Alternately, this question could be approached by plugging in the answer choices to see which works and does not work.