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← Isolate the Absolute Value - Visualizing Algebra

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Showing Revision 2 created 05/24/2016 by Udacity Robot.

  1. But where does this show up in my equation? If we subtract 4 from both sides,
  2. we're going to isolate the absolute value. We'll get the distance of p plus 3
  3. alone. This is where the 8 shows up. The absolute value or the distance of p
  4. plus 3 from 0 must be 8. When solving absolute value equations, we need to make
  5. sure we get the absolute value symbol on one side of the equation alone. That
  6. way, we can represent the distance. Once we isolate the absolute value, we want
  7. to check. We want to make sure that it's greater than or equal to 0. Remember,
  8. distance is always positive, so if we had a negative answer on this side, there
  9. would be any number that could make it true, there'd be no solution. This is a
  10. difficult concept and it's one that we'll stumble upon, too, later.
  11. So now, we're back into the same case before. The value of p plus 3 could be 8
  12. units to left of 0 at negative 8, or it could be 8 units to the right of 0, at
  13. positive 8. So, let's split this equation up into 2 equations, setting p plus 3
  14. to negative 8 and p plus 3 equal to positive 8. Just like from before. And at
  15. this point, you might even be able to solve it in your head, which is great. For
  16. more complicated questions, it's best to stick to the equation solving.
  17. Subtracting 3 from both sides, p could equal 5. And subtracting 3 from both
  18. sides, p could equal negative 11. So, the solution set or the values for p, are
  19. negative 11 and 5. And just like all our other equations, we can check these
  20. values in our original equation to see if we are right. That's one of the
  21. beauties of mathematics. This can help build your confidence in math. If this
  22. don't check, maybe it's a good idea to look back at your work. You might rethink
  23. your process or catch a small error.