Final answer:
To find the value of x for which the segments JK and RS are congruent, set their lengths equal to each other and solve for x.
Step-by-step explanation:
To find the value of x for which the segments JK and RS are congruent, we need to set their lengths equal to each other:
2x-9 = -4x+30
Adding 4x and 9 to both sides gives:
6x = 39
Dividing both sides by 6 gives:
x = 6.5
Therefore, when x is equal to 6.5, the segments JK and RS are congruent.