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20 Mar 2022, 06:55
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If x is a nonzero integer, which of the following must be true:
I) 3 < 3 + x
II) −x <0
III) x < 2x
A) none
B) I only
C) III only
D) II and III
E) I, II and III
I) 3 < 3 + x
II) −x <0
III) x < 2x
A) none
B) I only
C) III only
D) II and III
E) I, II and III
20 Mar 2022, 07:08
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If we subtract 3 on both sides of I, multiply by -1 on both sides of II (reversing the inequality when we do), and subtract x on both sides of III, each of I, II and III can be rewritten to say "x > 0". Since all we know is that x is a nonzero integer, we have no idea if x > 0 is true or false, so none of the three items needs to be true.
