Question

l is between m and k. ml = x + 2, lk = 2x - 8, and mk = 15. draw and label the segment. x = 7 lk =

Explanation:

Step1: Apply segment - addition postulate

Since \(L\) is between \(M\) and \(K\), we have \(ML + LK=MK\). Substitute the given expressions: \((x + 2)+(2x-8)=15\).

Step2: Simplify the left - hand side

Combine like terms: \(x+2x + 2-8=3x - 6\). So, \(3x-6 = 15\).

Step3: Solve for \(x\)

Add 6 to both sides: \(3x=15 + 6=21\). Then divide both sides by 3: \(x=\frac{21}{3}=7\).

Step4: Find the length of \(LK\)

Substitute \(x = 7\) into the expression for \(LK\). \(LK=2x-8\), so \(LK=2\times7-8=14 - 8=6\).

Answer:

\(LK = 6\)