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valiyuh

  • 2 years ago

m is the segment bisector of segment JK . JM= 1/8x , and JK= 3/4x-6 . How do i find MK? Help?

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  1. mathstudent55
    • 2 years ago
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    What does segment bisector mean?

  2. valiyuh
    • 2 years ago
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    its a line that divides a segment in half?

  3. mathstudent55
    • 2 years ago
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    Right. In this case, I think M is simply a point, but it still cuts the segment JK into two congruent segments.

  4. mathstudent55
    • 2 years ago
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    |dw:1377144056587:dw|

  5. mathstudent55
    • 2 years ago
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    Ok?

  6. mathstudent55
    • 2 years ago
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    Since M is a bisector, what do you know about the length of JM and the length of KM?

  7. valiyuh
    • 2 years ago
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    Well i know that since m is the bisector both sides are equal which mean that since JM is 1/8x MK is also 1/8x

  8. mathstudent55
    • 2 years ago
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    Good. |dw:1377144680791:dw|

  9. mathstudent55
    • 2 years ago
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    Form the figure you see that JM + MK = JK, right?

  10. valiyuh
    • 2 years ago
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    yes .

  11. mathstudent55
    • 2 years ago
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    Great. Below JM, MK, and JK, can you write what each one is equal to? Copy my line below and write it below that line. JM + MK = JK

  12. valiyuh
    • 2 years ago
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    1/8x + 1/8x = 3/4x-6 like this?

  13. mathstudent55
    • 2 years ago
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    Exactly. That is the equation you must solve now to find x.

  14. mathstudent55
    • 2 years ago
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    \( \dfrac{1}{8}x + \dfrac{1}{8}x = \dfrac{3}{4}x - 6\) Solve for x.

  15. valiyuh
    • 2 years ago
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    This is the part were im getting confused? Do i add both 1/8x to get 2/8x? or am i wrong?

  16. mathstudent55
    • 2 years ago
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    Yes, you are correct. \(\dfrac{2}{8}x = \dfrac{3}{4}x - 6 \) The fraction on the left can be reduced.

  17. valiyuh
    • 2 years ago
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    alright so now i subtract the 3/4 to the other side so now its 2/8 - 3/4?

  18. mathstudent55
    • 2 years ago
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    Why don't you reduce the 2/8 fraction first?

  19. mathstudent55
    • 2 years ago
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    \(\dfrac{1}{4}x = \dfrac{3}{4}x - 6 \)

  20. mathstudent55
    • 2 years ago
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    Now the fractions have a common denominator. Now you can subtract (3/4)x over to the left side.

  21. valiyuh
    • 2 years ago
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    it gave me -2x=-6?

  22. mathstudent55
    • 2 years ago
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    What happened to the denominator of 4? You subtracted 1/4 - 3/4, not 1 - 3.

  23. mathstudent55
    • 2 years ago
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    \(\dfrac{1}{4}x - \dfrac{3}{4}x = - 6 \) \(-\dfrac{2}{4}x = - 6 \)

  24. valiyuh
    • 2 years ago
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    oh okay i see and from there i cancel the -2/4x and take it to the other side having -6/-2/4 right?

  25. mathstudent55
    • 2 years ago
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    Now you multiply both sides by -4/2.

  26. mathstudent55
    • 2 years ago
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    \( -\dfrac{4}{2}\left( -\dfrac{2}{4}x \right) = -\dfrac{4}{2}(- 6) \)

  27. mathstudent55
    • 2 years ago
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    Did you get an answer for x?

  28. valiyuh
    • 2 years ago
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    12?

  29. mathstudent55
    • 2 years ago
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    Correct.

  30. mathstudent55
    • 2 years ago
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    After you multiply out the right side, you get x = 12. That's not the final answer of the problem, because the problem asks what is MK.

  31. valiyuh
    • 2 years ago
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    yes thats correct.

  32. mathstudent55
    • 2 years ago
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    Above, you had written an expression for MK in terms of x. Now you know x, so you can find MK. MK = (1/8)x, and x = 12, so what is MK?

  33. valiyuh
    • 2 years ago
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    1.5?

  34. mathstudent55
    • 2 years ago
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    Yes. MK = 12/8 = 1.5

  35. mathstudent55
    • 2 years ago
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    You got it! Great job.

  36. valiyuh
    • 2 years ago
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    Thank you so much you really helped me !(:

  37. mathstudent55
    • 2 years ago
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    You are very welcome.

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