Question

k is the mid - point of $overline{jl}$. if $kl = 10x - 8$ and $jl = 18x - 5$, what is $jl$? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since \(K\) is the mid - point of \(\overline{JL}\), then \(JL = 2KL\). So, \(18x−5 = 2(10x - 8)\).

Step2: Expand the right - hand side

Expand \(2(10x - 8)\) to get \(20x-16\). The equation becomes \(18x−5 = 20x - 16\).

Step3: Solve for \(x\)

Subtract \(18x\) from both sides: \(-5=2x - 16\). Then add 16 to both sides: \(2x=11\), so \(x=\frac{11}{2}\).

Step4: Find the value of \(JL\)

Substitute \(x = \frac{11}{2}\) into the expression for \(JL\): \(JL=18x - 5=18\times\frac{11}{2}-5\). First, \(18\times\frac{11}{2}=9\times11 = 99\). Then \(JL=99 - 5=94\).

Answer:

94