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37 votes
If K is the midpoint of JL, JK = 8x + 11 and KL = 14x – 1, find JL.​

If K is the midpoint of JL, JK = 8x + 11 and KL = 14x – 1, find JL.​-example-1
User Adrianmcmenamin
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3.1k points

1 Answer

27 votes
27 votes

Answer:


JL=54

Explanation:

We are given that K is the midpoint of JL. Using this information, we want to find JL.

By the definition of midpoint, this means that:


JK=KL

Substitute them for their equations:


8x+11=14x-1

Solve for x. Subtract 8x from both sides:


11=6x-1

Add 1 to both sides:


6x=12

And divide both sides by 6. Hence:


x=2

JL is the sum of JK and KL. Hence:


JK+KL=JL

Since JK = KL, substitute either one for the other:


JK+(JK)=2JK=JL

Substitute JK for its equation:


2(8x+11)=JL

Since we know that x = 2:


2(8(2)+11)=2(16+11)=2(27)=54=JL

Thus:


JL=54

User Kremena
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3.4k points