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Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

(absolute value of x minus 5) is less than or equal to 2.How many integers satisfy the inequality above?

(A) None
(B) One
(C) Two
(D) Three
(E) Five

答案和解析

答案：E

解析：

The inequality (absolute value of x minus 5) is less than or equal to 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 (absolute value of x minus 5) is less than or equal to 2.