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.