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

1. mathstudent55

What does segment bisector mean?

2. valiyuh

its a line that divides a segment in half?

3. mathstudent55

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

4. mathstudent55

|dw:1377144056587:dw|

5. mathstudent55

Ok?

6. mathstudent55

Since M is a bisector, what do you know about the length of JM and the length of KM?

7. valiyuh

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

Good. |dw:1377144680791:dw|

9. mathstudent55

Form the figure you see that JM + MK = JK, right?

10. valiyuh

yes .

11. mathstudent55

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

1/8x + 1/8x = 3/4x-6 like this?

13. mathstudent55

Exactly. That is the equation you must solve now to find x.

14. mathstudent55

$$\dfrac{1}{8}x + \dfrac{1}{8}x = \dfrac{3}{4}x - 6$$ Solve for x.

15. valiyuh

This is the part were im getting confused? Do i add both 1/8x to get 2/8x? or am i wrong?

16. mathstudent55

Yes, you are correct. $$\dfrac{2}{8}x = \dfrac{3}{4}x - 6$$ The fraction on the left can be reduced.

17. valiyuh

alright so now i subtract the 3/4 to the other side so now its 2/8 - 3/4?

18. mathstudent55

Why don't you reduce the 2/8 fraction first?

19. mathstudent55

$$\dfrac{1}{4}x = \dfrac{3}{4}x - 6$$

20. mathstudent55

Now the fractions have a common denominator. Now you can subtract (3/4)x over to the left side.

21. valiyuh

it gave me -2x=-6?

22. mathstudent55

What happened to the denominator of 4? You subtracted 1/4 - 3/4, not 1 - 3.

23. mathstudent55

$$\dfrac{1}{4}x - \dfrac{3}{4}x = - 6$$ $$-\dfrac{2}{4}x = - 6$$

24. valiyuh

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

Now you multiply both sides by -4/2.

26. mathstudent55

$$-\dfrac{4}{2}\left( -\dfrac{2}{4}x \right) = -\dfrac{4}{2}(- 6)$$

27. mathstudent55

Did you get an answer for x?

28. valiyuh

12?

29. mathstudent55

Correct.

30. mathstudent55

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

yes thats correct.

32. mathstudent55

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

1.5?

34. mathstudent55

Yes. MK = 12/8 = 1.5

35. mathstudent55

You got it! Great job.

36. valiyuh

Thank you so much you really helped me !(:

37. mathstudent55

You are very welcome.