<p>-0--------x---1-------------2-------></p>
<p>On the number line above, is the coordinate of the point shown. Which of the following must be true?</p>
<p>I. lxl <1
II. lx-2l >1
III. lxl + lx-1l = 1</p>
<p>(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III</p>
<p>Answer is E, how so? I thought it's only I</p>
<p>Because x lies between 0 and 1, you can plug in 0 or 1 (each in their own turn) for x, and see that each statement is true for those extreme values, so is true for the values in between, as well.</p>
<p>But for III, if i plug in 0.8
.8+ (.8-1) = .6
if x = .8, the answer is not 1</p>
<p>ohh, I see what I did wrong LOL</p>
<p>thanks anyway！</p>
<p>Since x is between 0 and 1 it must be a fraction and thus its absolute must be less than 1 making I correct.</p>
<p>Since x must be a positive fraction between 0 and 1 and any fraction minus 2 must give you a number that is between -1 and -2, its absolute (the resulting number as positive) must be between 1 and 2 and thus greater than 1, making II correct.</p>
<p>Again x is a positive fraction. No matter what x is, the equation in III has to work out the same every time as equal to 1. If x is 1/2, x - 1 is -1/2 whose absolute is 1/2 and thus the addition of the two equals1. If x is 1/4, then x-1 is -3/4 whose absolute is 3/4 and the additon of 1/4 + 3/4 = 1. Thus III must also be correct.</p>