Question

a line segment, k is between j and l. if jk = x - 2, kl = 8, and jl = 3x - 18, what is jl?
mplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use the segment addition postulate

Since \(K\) is between \(J\) and \(L\), \(JK + KL=JL\). Substitute the given expressions: \((x - 2)+8 = 3x-18\).

Step2: Simplify the left - hand side of the equation

Simplify \((x - 2)+8\) to \(x+( - 2 + 8)=x + 6\). So the equation becomes \(x + 6=3x-18\).

Step3: Solve for \(x\)

Subtract \(x\) from both sides: \(x - x+6=3x - x-18\), which gives \(6 = 2x-18\). Then add \(18\) to both sides: \(6 + 18=2x-18 + 18\), so \(24 = 2x\). Divide both sides by \(2\): \(x=\frac{24}{2}=12\).

Step4: Find the length of \(JL\)

Substitute \(x = 12\) into the expression for \(JL\). Since \(JL = 3x-18\), then \(JL=3\times12-18\). First, calculate \(3\times12 = 36\), then \(36-18 = 18\).

Answer:

\(18\)