<p>What are all values of x for which x - 3 > 9 - x^2?</p>
<p>Okay, I have two ways that I can do this with, and I come out with two different answers. I have simplified the steps so I could just show you the point of my question.</p>
<p>1st way:</p>
<p>x - 3 > 9 - x^2</p>
<p>0 > 9 - x^2 - x +3</p>
<ul>
<li><p>x^2 - x +12 < 0</p></li>
<li><p>4 < x < 3</p></li>
</ul>
<p>2nd Way:</p>
<p>x - 3 > 9 - x^2</p>
<p>x^2 + x - 3 - 9 > 0</p>
<p>X^2 + x - 12 > 0</p>
<p>-4 > x or x > 3</p>
<p>Which way is correct and why? I'm really lost on this one. Thanks in advance for anyone who helps me!</p>
<p>That’s ok, except the answer in 1st way.
Just look: whole inequality in line before has to be less than 0. Your answer would be correct for X^2 - X + 12 greater than 0.
x^2 - x +12 < 0 (1st method) is the same as x^2 + x - 12 > 0 (from second one). Second is just multiplied by -1. Conclusion: answer must be the same in both.</p>
<p>thanks a lot ivydreamerr for your answer, but I have to tell you that your answer is wrong because the two equations, as I said in my question, do not yield similar results. However, I discovered that the second way was correct. I tried plugging in 1 for x in the original equation and the answer turned out wrong, but when I plugged in -5, for example, the answer turned out correct. I’m still lost on why the 1st way yields an incorrect result and is not the solution. Any help on this is greatly appreciated. :)</p>
<p>One equation must give the same answer with any correct method. Well, that’s math
As i’ve said before, everything is correct and the answer from 2nd method is the right one. Your only mistake is the step between - x^2 - x +12 < 0 and - 4 < x < 3 in first method. Only answer is incorrect. Look at RyanMK’s reply.</p>
<p>For it to be less than 0, 1 and only 1 of the terms must be negative. The left half is less than 0 when x<4, and the right half is less than 0 when x>3.</p>
