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anonymous

  • one year ago

solve the equation. check for extraneous solutions. will fan and medal

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  1. anonymous
    • one year ago
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    \[9\left| 9-8x \right|=2x+3\]

  2. SolomonZelman
    • one year ago
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    well, you will get two results: \(9\left| 9-8x \right|=2x+3\) \(9(9-8x )=2x+3\) OR \(9(9-8x )=-2x-3\)

  3. SolomonZelman
    • one year ago
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    solve each case individually.

  4. anonymous
    • one year ago
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    i dont know where to start. will you walk me through it?

  5. SolomonZelman
    • one year ago
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    well, expand the right side in case 1

  6. SolomonZelman
    • one year ago
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    I mean the left side (not the right side)

  7. anonymous
    • one year ago
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    would you move the x to the left side first?

  8. SolomonZelman
    • one year ago
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    \(9(9-8x )=2x+3\) \(9\cdot9-9\cdot8x =2x+3\) \(81-72x =2x+3\)

  9. SolomonZelman
    • one year ago
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    So in case two you would have the same, but the right side would be -2x-3

  10. SolomonZelman
    • one year ago
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    Solve for each: \(81-72x =2x+3\) \(81-72x =-2x-3\)

  11. anonymous
    • one year ago
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    x would go on the left side?

  12. SolomonZelman
    • one year ago
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    you can add 72x to both sides in case 2 and case 1

  13. anonymous
    • one year ago
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    leaving us with 81=74x+3

  14. SolomonZelman
    • one year ago
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    two cases: \(81-72x =2x+3\) \(81-72x+72x =2x+72x+3\) \(81=74x+3\) right!

  15. SolomonZelman
    • one year ago
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    then subtract 3 from both sides.

  16. anonymous
    • one year ago
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    78=74x?

  17. SolomonZelman
    • one year ago
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    yes, so x=?

  18. anonymous
    • one year ago
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    74/78?

  19. SolomonZelman
    • one year ago
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    yes

  20. anonymous
    • one year ago
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    what about in the second case?

  21. SolomonZelman
    • one year ago
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    Now in case 2: \(81-72x =-2x-3\)

  22. SolomonZelman
    • one year ago
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    you also add 72x to both sides, THEN, add 3 to both sides

  23. anonymous
    • one year ago
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    x=70/84?

  24. SolomonZelman
    • one year ago
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    oh the first one is incorrect, and this one too

  25. anonymous
    • one year ago
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    noooo

  26. SolomonZelman
    • one year ago
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    when in case one you have: 78=74x you divide by 74 on both sides, and thus x=78/74 (not 74/78)

  27. SolomonZelman
    • one year ago
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    And in case two you made the same mistake

  28. anonymous
    • one year ago
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    so it would be 84/70?

  29. SolomonZelman
    • one year ago
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    Yes, for case 2.

  30. SolomonZelman
    • one year ago
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    And they are not extraneous.

  31. SolomonZelman
    • one year ago
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    let me say correctly what would have been extraneous:

  32. SolomonZelman
    • one year ago
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    Any x-solution, in this case, that is equal to \(C\) that satisfies: \(C<-2/3\)

  33. SolomonZelman
    • one year ago
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    because if x is less than -2/3 then 2x+3 is negative, and absolute value can NOT e equal to negative (since absolute value is really a distance)

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