Question

point k is on line segment \\(\overline{jl}\\). given \\(jl = 4x + 2\\), \\(kl = 5x - 6\\), and \\(jk = 3x\\), determine the numerical length of \\(\overline{jk}\\).

Explanation:

Step1: Use segment addition postulate

Since K is on \( \overline{JL} \), we have \( JK + KL = JL \). Substituting the given expressions: \( 3x + (5x - 6) = 4x + 2 \).

Step2: Simplify and solve for x

Combine like terms: \( 8x - 6 = 4x + 2 \). Subtract \( 4x \) from both sides: \( 4x - 6 = 2 \). Add 6 to both sides: \( 4x = 8 \). Divide by 4: \( x = 2 \).

Step3: Find length of \( \overline{JK} \)

Substitute \( x = 2 \) into \( JK = 3x \): \( JK = 3(2) = 6 \).

Answer:

6