Question

Which of the following statements says that a number is between -3 and 3? | x| < 3 | x| = 3 | x| > 3

Answer 1

$\underline {\pink { Absolute \:value \:of \:a \:real \: number :}}$

The absolute value of a real number is always positive .

If x € R ,then the absolute value of x is denoted by |x|.

$\underline {\pink { Properties \:of \: modulus :}}$

1. |x| < a => -a < x < a ( a> 0 )
2. |x|≤a => -a ≤ x ≤ a ( a > 0 )
3. |x| > a => x > a or x < -a

Here, a = 3 > 0

Therefore.,

|x| > 3 => x > 3 Or x < -3

i.e ., The number is between -3 and 3 if |x| > 3.

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