If \( k \) is the midpoint of \( JL \), \( JK = 8x + 11 \) and \( KL = 14x - 1 \), find \( JL \).

By setting the equation '8x + 11 = 14x - 1', we can find the value of x. After finding x, substitute it into any of the original equations to find the length of either JK or KL (these are half of JL). So, JL is twice the length of JK or KL, which we find by adding JK and KL. ;

Answered by Qwship | 2024-06-18

I f K i s t h e mi d p o in t o f J L , t h e n : J K = 2 1 ​ J L an d K L = 2 1 ​ J L t h ere f ore : 8 x + 11 = 14 x − 1 8 x − 14 x = − 1 − 11 − 6 x = − 12 x = − 12 : ( − 6 ) x = 2 J L = 2 J K ⇒ J K = 2 ⋅ ( 8 ⋅ 2 + 11 ) = 2 ⋅ ( 16 + 11 ) = 2 ⋅ 27 = 54 ​

Answered by Anonymous | 2024-06-24

To find the length of segment JL, we set JK and KL equal because K is the midpoint. Solving the equation gives us x = 2, and subsequently, we find JK = 27. Therefore, JL, which is the sum of JK and KL, is equal to 54.
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Answered by Anonymous | 2024-08-27