Suppose point J is between points H and K. If HJ = 6x - 5, JK = 4x - 6, and KH = 129, find the value of x and the length of each segment.
After you made your sketch, it should be obvious that
6x-5 + 4x-6 = 129
solve for x, then evaluate 6x-5 and 4x-6
x=14
thank you
correct, so the two segments are
6x-5 = 6(14) - 5 = 79
4x - 6 = 4(14)-6 = 50
note that 79+50 = 129
To solve this problem, we can use the fact that the sum of the lengths of two segments is equal to the length of the entire line segment they are a part of. In this case, the lengths of segments HJ, JK, and KH add up to the length of line segment HK.
First, let's express the length of HK in terms of x:
HK = HJ + JK
Substituting the given expressions for HJ and JK, we have:
HK = (6x - 5) + (4x - 6)
Next, we can substitute the given value for KH:
KH = HK
Substituting the expression for HK derived above, we have:
129 = (6x - 5) + (4x - 6)
Now, we can simplify and solve for x:
129 = 6x - 5 + 4x - 6
129 = 10x - 11
140 = 10x
x = 14
Now that we have found the value of x, we can substitute it back into the expressions for HJ and JK to find their lengths.
HJ = 6x - 5
HJ = 6(14) - 5
HJ = 84 - 5
HJ = 79
JK = 4x - 6
JK = 4(14) - 6
JK = 56 - 6
JK = 50
Finally, we can check our answer by adding the lengths of HJ, JK, and KH:
HJ + JK + KH = 79 + 50 + 129 = 258
Since the sum of the lengths of the segments is equal to the length of line segment HK, our answer is correct.
Therefore, the value of x is 14, the length of HJ is 79, the length of JK is 50, and the length of KH is 129.