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← Graphing Any Linear Inequality - Visualizing Algebra

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

  1. Sometimes we might run into inequalities that are not in slope intercept form.
  2. We can handle these inequalities much like we did linear equations. We can try
  3. and solve this inequality for y. First I subtract x from both sides, to get
  4. negative 4y is less than or equal to negative 12 minus x. I'm going to rearrange
  5. the terms here. So, I'll have negative 4y less than or equal to negative x minus
  6. 12. Notice that the sign in front of the term stays with it. The x is still
  7. negative, as before. And this 12 is still negative, as before. Finally, we
  8. divide every term by negative 4. Here's where we need to be very careful. We're
  9. dividing by a negative, and this is an inequality symbol. Just like from before,
  10. we know we need to reverse the inequality sign. The other thing we want to watch
  11. out for are the negatives on the other side. A negative divided by a negative
  12. makes a positive, and the same is true here. So we're left with, y is greater
  13. than or equal to 1 4th x plus 3. And don't forget about that 1 as the
  14. coefficient in front of x. That's how we can get positive 1 4th. Now that we
  15. have this inequality, we can graph it just like before. We'll start by plotting
  16. the line. Then we'll determine whether or not that line should be dashed or
  17. solid. And finally, we can determine the region by using a test point. We plug
  18. in a point to see if it makes the inequality true. If it does, we want that
  19. region. If not, we'll take the other one.