Question

The segment JL has a definite length of [Drop Down 1]. Segments JK and KL have both definite lengths of [Drop Down 2] and [Drop Down 3], respectively. Both segments are [Drop Down 4]. JL=6x-8, JK=2x, and KL=2x+2.

a) 12 units
b) 3 units
c) 5 units
d) 6 units

Answer 1

To find the length of JL, the equations for JL, JK, and KL were used to set up and solve an equation resulting in x being 5. Substituting x back into the equation for JL gives a length of 22 units for segment JL.

Step-by-step explanation:

The student's question pertains to finding the length of the segment JL given the expressions for segments JL, JK, and KL. To solve for the lengths of these segments, we set up an equation using the fact that the sum of the lengths of segments JK and KL equals the length of segment JL, because they are consecutive segments of the line.

So we have JL = JK + KL
6x - 8 = 2x + 2x + 2
6x - 8 = 4x + 2.

By rearranging the equation, we subtract 4x from both sides and add 8 to both sides to solve for x:
2x = 10
x = 5.

Now that we have the value of x, we can determine the length of segment JL by substituting x back into the equation JL=6x-8:
JL = 6(5) - 8 = 30 - 8 = 22 units.