Hi,
When solving for questions where you have two absolute values added to each other, the best way is to work with distances traveled on the number line.
The absolute value is defined as the distance traveled from the origin on the number line, so if |x - 2| = 5, this means that the distance traveled from the origin i.e. 2 has to be 5 units. Imagine a person standing at 2 on the number line and having to travel a distance of 5 units from 2. The person can move left to a distance of 5 units and will end up at -3 or he can move right to a distance of 5 units and will end up at 7. These would be the solutions to the equation |x - 2| = 5.
Now let us use this basic understanding to solve the question given.
|b - 2| + |b + 8| = 10
The question says that the total distance traveled from 2 to -8 is 10 units. So if we imagine two people, one who is at 2 and the other who is at -8 the total distance that needs to be covered by both together is 10 units. So the only way this can be done is if both of them meet art any point in between 2 and -8.
So the question just asks us if b is between -8 and 2.
Attachment:
Capture.PNG [ 93.31 KiB | Viewed 6343 times ]
Statement 1 and Statement 2 together give us this.
Answer: C _________________
Crackverbal Prep Team
www.crackverbal.com