Question

point k is on line segment jl. given jl = 4x, jk = 2x + 3, and kl = x, determine the numerical length of kl.

Explanation:

Step1: Use the segment addition postulate

Since \(K\) is on segment \(JL\), we know that \(JL = JK+KL\).
Substitute the given expressions: \(4x=(2x + 3)+x\).

Step2: Simplify the equation

Combine like - terms on the right - hand side: \(4x=2x+x + 3\), so \(4x=3x + 3\).
Subtract \(3x\) from both sides: \(4x-3x=3x + 3-3x\).
We get \(x = 3\).

Step3: Find the length of \(KL\)

Since \(KL=x\), and \(x = 3\).

Answer:

\(3\)