Mathematics > Standard Multiple Choice
Read the following SAT test question and then click on a button to select your answer.
|X—5|≤2
How many integers satisfy the inequality above?
Answer Choices
(A) None
(B) One
(C) Two
(D) Three
(E) Five
The correct answer is E
Explanation
The inequality |X—5|≤2 is equivalent to -2≤X—5≤2. Adding 5 to each term of this inequality gives -2+5≤X—5+5≤2+5, which is equivalent to 3≤X≤7 There are five integers (3, 4, 5, 6 and 7) that satisfy this inequality, and so there are five integers that satisfy |X—5|≤2.
