Answer: Given the information:
JK = 2x + 7
KL = 19
JL = 7x - 19
We know that the segments JK and KL together form the segment JL, so we can set up an equation:
JK + KL = JL
Substitute the given values:
2x + 7 + 19 = 7x - 19
Combine like terms:
2x + 26 = 7x - 19
Subtract 2x from both sides:
26 = 5x - 19
Add 19 to both sides:
45 = 5x
Now, divide both sides by 5:
x = 9
Now that we know the value of x, we can substitute it back into the expression for JK:
JK = 2x + 7
JK = 2 * 9 + 7
JK = 18 + 7
JK = 25
So, the length of JK is 25.