Question

Which compound inequality is equivalent to the absolute value inequality ? –6 > b and b > 6 b > –6 or b < 6 –6 < b and b > 6 b < –6 or b > 6

Answer 1

Just 6 because negative 6 is in between the positive 6

Answer 2

Answer:

The option 2  

b > -6 or b < 6 ⇒ |b| < 6    

Step-by-step explanation:

Given the compound inequality

we have to choose the inequality which is equivalent to the absolute value inequality.

An absolute value inequality

It is an inequality that has an absolute value sign with a variable inside.

In other words, for any real numbers x and y,

if | x | < y , then a < b and a > -b

Option 1: -6 > b and b > 6

Not possible as b can not be greater than 6 if it is less than -6

⇒ No solution exits

Option 2: b > -6 or b < 6

⇒ |b| < 6

which is absolute inequality.

Option 3: -6 < b and b > 6

This gives b is greater than 6 not an absolute inequality.

Option 4: b < –6 or b > 6

Not possible as b can not be greater than 6 if it is less than -6

⇒ No solution exits

Hence, option 2 is correct.