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?
(A) None
(B) One
(C) Two
(D) Three
(E) Five
The correct answer is E
Explanation
The inequality |x-5|<=2 is equivalent to negative 2 is less than or equal to (x minus 5) is less than or equal to 2. Adding 5 to each term of this inequality gives (negative 2 plus 5) is less than or equal to (x minus 5 plus 5) is less than or equal to (2 plus 5), which is equivalent to 3 is less than or equal to x is less than or equal to 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.