DS Absolute value equation: What is the value of y?

[jlucero]

I am confused to understand when do we really consider an absolute value to be "absolute values are always positive" and "absolute values have two versions - positive as we as negative"?

Can someone please explain in context to this question?

It depends on whether you're trying to solve what's going to be inside vs outside of the absolute value. If you're trying to figure out what's coming out of the AV, then you only need to concern yourself with the positive value

|-2| = x; x = 2

On the other hand, if you're trying to solve what values could be inside of the absolute value, then you have to solve the equations twice, once when the inside would be a positive value. And once when the inside would be a negative value, changed by the absolute value

|x| = 2; x = 2 or -2

[TimH134]

What if the question were changed...(y + 2)

What is the value of y?

(1) 3|x^2 - 4| = y + 2

(2) |3 - y| = 11

How do you reason Statement 1?

[RonPurewal]

wouldn't change anything; still (c).

• statement 1 is still clearly insufficient

• statement 2 gives two different values of y

• one of those two values makes statement 1 impossible, for the same reason as before (absolute value = negative). so with the two statements combined, you're left with a single value of y.