The modulus or absolute value is basically the distance from the given point to zero. While this is the more "official" version of the modulus or absolute value, you just need to remember two things about the modulus and you're done:
a. x is positive or zero makes |x| = x. Example: |3| = 3; |2343576| = 2343576. The distance from one positive number to zero is exactly that number
b. x is negative makes |x| = -x. Example: |-5| = -(-5) = 5, |-10| = -(-10) = 10. The distance from a negative number is the opposite of that number, since a distance CAN'T be negative.
Now, coming back to the question:
You get that |x + 4| = 2. Now apply what we've learned and you get two cases:
a. x + 4 is positive or zero means that |x + 4| = x + 4 = 2 makes x = -2. EXTREMELY IMPORTANT: back-check to see if your answer is consistent with the initial assumption that x + 4 is positive. When x = -2, x + 4 = 2, which is indeed positive. This means that x = -2 is a good answer.
b. x + 4 is negative makes |x + 4| = -x - 4 = 2. This means that -x = 6 or x = -6. Again we back-check: -6 + 4 = -2, which is negative.
As you can see, there are two answers to this problem: x = -2 or x = -6.
Now, getting to our stmts:
1. means that x is neither 2 or -2. This eliminates x = -2 and leaves x = -6. So 1 is sufficient.
2. x^2 = 36 makes x 6 or -6. This takes out x = -2, with answer x = -6.
So my answer is D
