Determine whether the following statement is always, sometimes, or never true. Give examples to justify your answer.
If x and y are both greater then zero and x > y, then -x < -y

Sometimes. Say x = 3 and y = 4. 3 + 4 = 7, 3 - 4 = -1. However, the subtraction problem can be greater than the addition if you add some negatives into the mix. Say x = 3 and y = -4. 3 + (-4) is the same as subtracting 4, which give you -1. However, when you subtract negative four, it's the same as adding four, which gives you seven.

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Determine whether the following statement is always, sometimes, or never true. Give examples to justify your answer. If x and y are both greater then zero and x > y, then -x < -y

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Determine whether the following statement is always, sometimes, or never true. Give examples to justify your answer.
If x and y are both greater then zero and x > y, then -x < -y