If x < 12, then it must be true that...  Choose one:
A) -x < -12 B) -x - 2 < 14 C) -x + 2 < -10 D) x + 2 < 10 E) x - 6 < 17
A. -x &lt; -12 --&gt; x&gt;12. Not true.   B. -x - 2 &lt; 14 --&gt; x&gt;-16. Not true, consider x=-20.   C. -x + 2 &lt; -10 --&gt; x&gt;12. Not true.   D. x + 2 &lt; 10 --&gt; x&lt;8. Not true, consider x=10.   E. x - 6 &lt; 17 --&gt; x&lt;23. Since given that x&lt;12, then x is for sure less than 13. Thus this statement must be true.   Answer: x - 6 &lt; 17.
<result>E</result>
If x < 12, then it must be true that...