Question

if kl = 11x, lm = 18x - 20, and km = 20x + 7, what is km? diagram of k---l---m with kl=11x, lm=18x-20, km=20x+7 simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

From the number line, we know that \( KL + LM = KM \). Substituting the given expressions: \( 11x+(18x - 20)=20x + 7 \)

Step2: Simplify the left - hand side

Combine like terms: \( 11x+18x-20=29x - 20 \). So the equation becomes \( 29x-20 = 20x+7 \)

Step3: Solve for x

Subtract \( 20x \) from both sides: \( 29x-20x-20=20x - 20x+7 \), which simplifies to \( 9x-20 = 7 \). Then add 20 to both sides: \( 9x-20 + 20=7 + 20 \), so \( 9x=27 \). Divide both sides by 9: \( x=\frac{27}{9}=3 \)

Step4: Find the length of KM

Substitute \( x = 3 \) into the expression for \( KM \), which is \( 20x+7 \). So \( KM=20\times3 + 7=60 + 7=67 \)

Answer:

67