Question

Which expression is equivalent to |b| >2?

Answer 1

|b| > 2 is equivalent to -2 > b > 2.

Explanation:

Definition of absolute value is:

The set of all points that satisfy the inequality |x| < c is the set of all points between c and -c except of -c and c.

In question statement , we observe that

x = b and c = 2.

Hence, the given inequality means the set of set of all points that is between 2 and -2 except 2 and -2.

hence, |b| > 2 is equivalent to -2 > b > 2.

Answer 2

The equivalent expression for |b| > 2 is {b : b < -2} ∪ {b : b > 2}.

Explanation:

The expression |x| < a is equivalent to -a < x < a and the expression |x| > a is equivalent to {x : x < -a} ∪ {x : x > a}.

This means, the set of all points that satisfy the inequality |x| < a is the set of all points between -a and a exclusive of -a and a.

The set of all points that satisfy the inequality |x| > a is the set of all points that are less than -a and the set of all points that are greater than a.

Hence, the equivalent expression for |b| > 2 is {b : b < -2} ∪ {b : b > 2}.