1. If |x|+|y| = 4 and x ≠= y, then x CANNOT be equal to
Answer: D
x cannot be equal to -5
Given the equation |x| + |y| = 4, the possible values of x and y must satisfy this condition while also ensuring that x is not equal to y. The value -5 would imply that |x| = 5, which cannot be true since that would require |y| to be -1, an impossible scenario.
A) 2
If x = 2, then |x| + |y| = 4 implies |y| = 2. In this case, y could equal 2 or -2. Since x ≠ y, it is possible for x to equal 2 while satisfying the equation.
B)
This option is blank and does not provide any relevant information to assess.
C) -2
If x = -2, then |x| + |y| = 4 implies |y| = 6. This means y could be 6 or -6, which allows for the condition that x ≠ y to hold true. Thus, x can equal -2.
D) -5
Setting x = -5 gives |x| = 5. In this case, |y| must equal -1, which is not possible since absolute values cannot be negative. Therefore, x cannot equal -5 under the given conditions.
Conclusion
The value -5 cannot be a solution for x because it leads to an invalid condition regarding the absolute value of y. Other options, such as 2 and -2, allow for valid solutions that adhere to the equation while respecting the constraint x ≠ y. Thus, -5 is the only option that definitively cannot be equal to x.