# Graphing Inequalities? Solution sets?

• Oct 21st 2007, 03:55 PM
Dunit0001
Graphing Inequalities? Solution sets?
Thanks for all your help...I don't understand this one....

How do I graph it?

x^2 < or = x + 12

I factored it into (x+3)(x-4) < or = 0

My teacher taught me to make number lines for each factor and put where the factor is positive or negative and I still don't get it. Can anyone explain how those sign graphs work?
• Oct 21st 2007, 04:07 PM
Jhevon
Quote:

Originally Posted by Dunit0001
Thanks for all your help...I don't understand this one....

How do I graph it?

x^2 < or = x + 12

I factored it into (x+3)(x-4) < or = 0

My teacher taught me to make number lines for each factor and put where the factor is positive or negative and I still don't get it. Can anyone explain how those sign graphs work?

you have: $x^2 \le x + 12$

$\Rightarrow x^2 - x - 12 \le 0$

just graph the parabola $y = x^2 - x - 12$ it will be easy to identify the interval where it is less than or equal to zero (on this interval, the graph will be below the x-axis). so the answer is the range of x's for which the graph is under the x-axis (this includes the end points, since we can be equal to zero)

this will indeed be easier if you consider the factors (x + 3)(x - 4). this is zero for x = -3, and x = 4. now check all regions in between those and on either side to see if the inequality holds (your professor was trying to emphasize the concept that we have a number less than zero if we have a positive times a negative, so just make sure one is negative while the other is positive)