If |x|+|y| = 4 and x ≠= y, then x CANNOT be equal to

Rationale

x cannot be equal to -5.

Given the equation |x| + |y| = 4, the possible values of |x| and |y| must sum to 4. Since x and y are not equal, the absolute values must be distinct. The value -5 would imply |x| = 5, which cannot satisfy the equation because it would require |y| to be -1, an impossible condition.

A (2) YOUR ANSWER

If x = 2, then |x| = 2. To satisfy |x| + |y| = 4, |y| must equal 2, which is valid as y can be either 2 or -2, keeping the condition x ≠ y true.

B (0) YOUR ANSWER

Setting x = 0 yields |x| = 0. This requires |y| to equal 4. Thus, y can be 4 or -4, which also maintains the condition x ≠ y, making this choice possible.

C (-2) YOUR ANSWER

If x = -2, then |x| = 2. Consequently, |y| must also equal 2, allowing y to be 2 or -2. Since this does not violate x ≠ y, this choice remains valid.

D (-5) CORRECT

Choosing x = -5 leads to |x| = 5. In this case, |y| would have to equal -1 to satisfy the equation |x| + |y| = 4, which is not possible since absolute values cannot be negative. Thus, this choice is not feasible.

Conclusion

The equation |x| + |y| = 4 restricts the possible values for x based on the requirements of absolute values. Among the options, only -5 fails to meet the criteria, as it leads to an impossible condition with |y|. Therefore, -5 is the value that x cannot equal under the specified conditions.

If |x|+|y| = 4 and x ≠= y, then x CANNOT be equal to

x cannot be equal to -5.

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