<p>Let [x] be defined as [x] = x^2 + x for all values of x. If [n] = [n+2], what is the value of n?</p>
<p>(A) -3/2
(B) -2/3
(C) 2/3
(D) 2
(E) 3</p>
<p>Why is it A?</p>
<p>Since I'm too lazy to go figure it out, I would probably just start plugging away, starting with A, haha.
Plug in -3/2 for x. (-3/2)^2 -3/2 = 0.75
Plug in -3/2 + 2 = 0.5 for x. (0.5)^2 + 0.5 = 0.75
0.75 = 0.75, hence A is the answer.</p>
<p>[n]=[n+2] can be rewritten as:</p>
<p>n^2 + n = (n+2)^2 + (n+2)</p>
<p>Then, expand (n+2)^2, so that the new equation is:</p>
<p>n^2 + n = n^2 + 4n + 4 + (n+2)</p>
<p>Combine like terms:</p>
<p>n^2 + n = n^2 + 5n + 6</p>
<p>Then solve:</p>
<p>n = 5n + 6
4n + 6 = 0
4n = -6
n = (-6/4) which simplifies to (-3/2)</p>
<p>[n]=n^2 + n and [n+2]=(n+2)^2 + (n+2)</p>
<p>n^2+n = (n+2)^2+n+2
n^2+n = (n^2+4n+4) +n+2
n^2+n = n^2+5n+6
n=5n+6
-4n=6
n=-3/2</p>
<p>km7289's process is more time efficient, but here it is:</p>
<p>n^2 + n = (n+2)^2 + (n+2)
n^2 + n = n^2+4n+4 + n+2
n^2 + n = n^2+5n+6
4n+6 = 0
4n = -6
n = -6/4 = -3/2</p>
<p>edit: LOL, I guess two people beat me to it ._.</p>
<p>Haha, all these solutions came to you at once. Do you understand now?</p>
<p>Hey I'm sitting in a car dealership, negotiating a hybrid purchase, so I dont feel too bad about being a late enterer.</p>
<p>But if I was taking it, I would have plugged answer choices into the original equation, but r3n there wanted a solution, so he got a number of them.</p>
<p>Yeah, I would have just plugged in as well. But it's probably still a good idea to learn how to solve that kind of problem, just in case a similar problem shows up as a grid-in problem.</p>
<p>Chris, what car are you looking at?</p>
<p>Civic Hybrid - pricey but its pretty cool.</p>
<p>ooooooo get a Prius...those things look amazing :D</p>
<p>Interior is kind of weird, though - but the start button, backup camera, bluetooth definitely cool. I am looking at Prius also, but I think the Civic wins on price alone.</p>
<p>I love the Prius! Especially the backup camera and the start button. You might want to check out tax returns on hybrids, because according to [url=<a href="http://www.fueleconomy.gov/feg/tax_hybrid_new.shtml%5Dthis%5B/url">http://www.fueleconomy.gov/feg/tax_hybrid_new.shtml]this[/url</a>], you can get a slightly higher return on the Prius. But I don't think it will amount to any overall difference in price.</p>
<p>The only complaint I had with hybrids was that they were small, but since some car manufacturers are starting to have hybrids of bigger cars (accord, camry, etc) I can't really complain anymore.</p>
<p>wait why does the [n] has to get replaced with [x]?</p>
<p>Let [x] be defined as [x] = x^2 + x for all values of x. If [n] = [n+2], what is the value of n?</p>
<p>Basically, x can be thought of as "any number," and n can be thought of as "a specific number."
[x] works so that if you have any old number, x, you could just plug in and you would get x^2 + x.
n is used to show an unknown number, n. n is the number that satisfies the expression [x] = [x+2], and in this case, when x = -3/2, that expression is satisfied, so n is -3/2.</p>
<p>There's really no difference; if that confuses you, you could very well rewrite the problem as:</p>
<p>Let [x] be defined as [x] = x^2 + x for all values of x. If [x] = [x+2], what is the value of x?</p>
<p>Basically x^2 + x = (x+2)^2 + (x+2)</p>
<p>Sorry if I suck at explaining : P</p>
<p>I think plug answer choices into the question is the best solution.</p>