Point J is between H and K on line HK. Use the given information to write an equation in terms of x. Solve the equation. Then find HJ and JK
HJ=5x-3
JK=x-9
KH=5x
Draw it
5x-3 + x-9 = 5 x
-12 + x = 0
x = 12
HJ = 5(12)-3 = 57
JK = x-9 = 3
To find the equation in terms of x, we can use the fact that the sum of HJ and JK is equal to KH.
HJ + JK = KH
Plug in the given expressions for HJ, JK, and KH:
(5x - 3) + (x - 9) = 5x
Simplify and solve for x:
6x - 12 = 5x
Subtract 5x from both sides:
x - 12 = 0
Add 12 to both sides:
x = 12
Now that we have found the value of x, we can plug it back into the expressions for HJ and JK to find their respective lengths.
HJ = 5(12) - 3 = 60 - 3 = 57
JK = (12) - 9 = 3
Therefore, HJ = 57 and JK = 3.
To solve this problem, we can first set up an equation using the given information about the lengths of the line segments.
We know that HJ + JK = HK. So, let's substitute the given expressions for HJ and JK into the equation:
(5x - 3) + (x - 9) = 5x
Now, we can solve this equation to find the value of x:
Combine like terms:
6x - 12 = 5x
Subtract 5x from both sides:
6x - 5x - 12 = 0
Subtract 5x from 6x:
x - 12 = 0
Add 12 to both sides:
x = 12
Now we have the value of x, which is 12. We can substitute this value back into the expressions for HJ and JK to find their lengths:
HJ = 5x - 3 = 5(12) - 3 = 60 - 3 = 57
JK = x - 9 = 12 - 9 = 3
So, HJ = 57 and JK = 3.