Final answer:
The equation |x| + 2 = -2 has no solution because the result of an absolute value is never negative, thus the smallest value that |x| + 2 can take on is 2, which is already greater than -2.
Step-by-step explanation:
The given equation involves the absolute value of a variable: |x| + 2 = -2. When dealing with absolute values, the expression inside the absolute value can either be positive or negative, but it always results in a non-negative number after the absolute value is applied. Thus, the smallest value |x| can take on is zero, which would make the left side of the equation |x| + 2 equal to 2 at minimum. Since 2 is already greater than -2, there is no possible way for |x| + 2 to equal -2. In other words, no matter what value of x you choose, once you apply the absolute value, the result will never be negative, and thus cannot be equal to -2 once 2 is added.
Therefore, the solution to this equation is No solution (Option A), because there does not exist a real number x that will satisfy the equation |x| + 2 = -2.