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.
