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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?

Answer Choices

Yep! That's right.

Explanation

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.

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