Question

k is the midpoint of $overline{jl}$. if $jk = x + 2$ and $jl = 3x - 4$, 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 \(JK=\frac{1}{2}JL\). So \(2JK = JL\).
Substitute \(JK=x + 2\) and \(JL = 3x-4\) into the equation \(2JK = JL\), we get \(2(x + 2)=3x-4\).

Step2: Expand the left - hand side

Expand \(2(x + 2)\) using the distributive property \(a(b + c)=ab+ac\). Here \(a = 2\), \(b=x\), \(c = 2\), so \(2(x + 2)=2x+4\).
The equation becomes \(2x + 4=3x-4\).

Step3: Solve for \(x\)

Subtract \(2x\) from both sides of the equation:
\(2x+4-2x=3x - 4-2x\), which simplifies to \(4=x - 4\).
Then add 4 to both sides: \(4 + 4=x-4 + 4\), so \(x = 8\).

Step4: Find the value of \(JL\)

Substitute \(x = 8\) into the expression for \(JL\): \(JL=3x-4=3\times8-4\).
\(JL=24 - 4=20\).

Answer:

20