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anonymous

  • one year ago

Solve the inequality |x-10| - 9 < -1 and graph The solutions. Then write the solutions as a comp

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  1. anonymous
    • one year ago
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    As a compound inequality.

  2. anonymous
    • one year ago
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    Pleaseeee helpppp!!!!

  3. anonymous
    • one year ago
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    Do you know the first steps to solve the inequality?

  4. anonymous
    • one year ago
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    No not sure

  5. anonymous
    • one year ago
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    First step, is to isolate the absolute value side!

  6. anonymous
    • one year ago
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    How do u exactly do that

  7. anonymous
    • one year ago
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    By removing everything that's not INSIDE the absolute value sign on the left side of the inequality!

  8. anonymous
    • one year ago
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    So u remove the -9 < -1?

  9. anonymous
    • one year ago
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    Just the -9 because the -1 is on the right side of the inequality. When I say inequality i mean the symbol in the middle that looks like this: <

  10. anonymous
    • one year ago
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    Do do I cross out the -9?

  11. anonymous
    • one year ago
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    No you can't just make the -9 disappear into nothing.

  12. anonymous
    • one year ago
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    You have to add it to both sides!

  13. anonymous
    • one year ago
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    So what do we do with the -9 to get rid of it?

  14. anonymous
    • one year ago
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    You have to add 9 to the left side and the right side. |x-10| - 9 < -1 + 9 +9

  15. anonymous
    • one year ago
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    By adding the opposite of -9 you can cancel it out with itself!

  16. anonymous
    • one year ago
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    So it would be 8?

  17. anonymous
    • one year ago
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    Yes! It would be 8 on the right side!

  18. anonymous
    • one year ago
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    So now do we work within the absolute value on the left side?

  19. anonymous
    • one year ago
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    So now we have |x-10| < 8 and now the absolute value sign has been isolated!

  20. anonymous
    • one year ago
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    Yes but you have to do something special to solve that absolute value. Do you know what's next?

  21. anonymous
    • one year ago
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    Ok so now what's the next step

  22. anonymous
    • one year ago
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    Multiply?

  23. anonymous
    • one year ago
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    Now you have to break the absolute value into "cases".

  24. anonymous
    • one year ago
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    How will we do that?

  25. anonymous
    • one year ago
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    |x-10| < 8 is broken down into x-10 < 8 and x-10 > -8|dw:1440964722548:dw|

  26. anonymous
    • one year ago
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    Notice how i didn't include the absolute value signs, and how the second one has the negative 8!!

  27. anonymous
    • one year ago
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    Why does it turn to -8?

  28. anonymous
    • one year ago
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    For the first "case" just rewrite the original problem. For the second "case" make everything on the right the opposite sign AND flip the inequality sign!

  29. anonymous
    • one year ago
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    See how < became > on the second one?

  30. anonymous
    • one year ago
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    U always have to do that?

  31. anonymous
    • one year ago
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    We do this in order to solve absolute value inequalities. And yes you always have to do that.

  32. anonymous
    • one year ago
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    Now do we subtract the x-10

  33. anonymous
    • one year ago
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    But ONLY if you have absolute values in your inequality!

  34. anonymous
    • one year ago
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    no just the -10 leave the x where it is

  35. anonymous
    • one year ago
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    So x-10 < 8 +10 +10

  36. anonymous
    • one year ago
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    So for the next step the x disappears?

  37. anonymous
    • one year ago
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    No we're trying to find what X is. Oh and by the way the 2 cases have nothing to do with each other!

  38. anonymous
    • one year ago
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    They are 2 different problems now

  39. anonymous
    • one year ago
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    I thought the new sign was >

  40. anonymous
    • one year ago
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    Only on the second case!

  41. anonymous
    • one year ago
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    We are working with the first case where everything stays the same!

  42. anonymous
    • one year ago
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    Oh ok

  43. anonymous
    • one year ago
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    If you do the second case you get x-10 > -8 +10 +10 x > 2

  44. anonymous
    • one year ago
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    So now we have the first case: x < 18 and the second case: x > 2

  45. anonymous
    • one year ago
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    We're still doing the first case right

  46. anonymous
    • one year ago
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    No the first and second ones are right there

  47. anonymous
    • one year ago
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    First Case: x < 18 Second case: x > 2

  48. anonymous
    • one year ago
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    See how they both have x? Couldn't we just write it like this then: 2 < x < 18 And that's your compound inequality!

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