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← Solution Intervals - College Algebra

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Showing Revision 2 created 05/25/2016 by Udacity Robot.

  1. I always need to use a table when I'm solving rational inequalities and
  2. quadratic ones for that matter, so here is my filled out table. Now I can just
  3. read off which of these regions contains x values that make this fraction or
  4. this rational expression negative. So that's just this first reqion, which is x
  5. is less than two, and the second region x is greater than 3. [inaudible] Since
  6. on a number line these two regions do not overlap, we have to use an or since no
  7. value of x can fall inside both regions. So the solution is, x is less than 2 or
  8. x is greater than 3. Let's take a second to think about how we could visualize
  9. this inequality using graphs. So here I've plotted 2 Equations. I plotted Y
  10. equals negative 16 X plus 48, over the quantity 3 minus 6, and the purple line
  11. is just the line Y equals 0. The X axis. We want to know according to our
  12. inequality when this line, the pink one, lies underneath the purple one. We want
  13. to know when the Y values of this curve drop below this curve. So we can see
  14. that, that's every part that's going to happen for all X values except for those
  15. in the very small portion of the curve that's up here. We can see that this
  16. matches the solution we came up with. This curve lies below this one, anywhere
  17. beyond this point, where x is equal to 3. And anywhere in this part of the
  18. graph. This line right here that represents the disconnect between these 2
  19. portions of the pink graph. Goes straight through the .20. And, in fact, this is
  20. the line, x equals 2. We can see that the entire part of the pink graph that's
  21. to the left of this, or that has x values less than 2, is underneath the purple
  22. curve. So this fits what we found. Awesome.