Question

Which expression is equivalent to |x| < 11?

Responses

x > –11 or x < 11

x > –11 or x < 11

x < –11 and x > 11

x < –11 and x > 11

x < –11 or x > 11

x < –11 or x > 11

x > –11 and x < 11

Answer 1

Which expression is equivalent to |x| < 11?

x > –11 and x < 11

Answer 2

x > -11 and x < 11

Explanation:

Find the absolute value of a number gives you its distance from zero, which is just the numerical parts of it. From this we can reason that the numbers between -11 and 11 have an absolute value less than 11, as they are the numbers that are less than 11 away from zero. This can be represented as -11 < x < 11, and can be separated into x > -11 and x < 11 (the "and" is because x has to fulfill both conditions of being greater than -11 and less than 11).