<p>Hi Guys. Could you help with the folowing question:
if 6<[x-3]<7 and x<0 ,what is one possible value of [x]?</p>
<p>I assume you meant to use the absolute value symbol here, as in |x|. Here are three possible solutions:</p>
<p>Solution by guessing: A bit of guessing and checking should lead you to something close to x = -3.5. Indeed, |-3.5 – 3| = |-6.5| = 6.5. So we see that x = -3.5 satisfies both conditions, and therefore we can grid in |x| = 3.5. </p>
<p>Quick solution: Just solve the equation x– 3 = -6.5, to get x = -3.5. So we have |x| = 3.5. </p>
<p>Algebraic solution: This is a bit tricky. Since x must be negative we want to solve the inequality -7 < x – 3 < -6. Adding 3 to each part gives us -4 < b < -3. So 3< |x| < 4. Therefore we can grid in any number between 3 and 4 (but 3 or 4 will be marked wrong!).</p>
<p>Thanks you Dr Steve.Yes I meant the absolute value symbol. The correct answer was 3<x<4.So 3.5 should be correct too.This question is from previous SAT test papers(2010-2011).I could not get the explanation but now I do.Thanks once again.</p>