Question

on a line segment, i is between k and m. if ki = 5x, im = 16x - 20, and km = 18x + 13, what is km? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

Since \( I \) is between \( K \) and \( M \), we have \( KI + IM = KM \). Substituting the given expressions: \( 5x + (16x - 20) = 18x + 13 \).

Step2: Simplify and solve for \( x \)

Combine like terms: \( 21x - 20 = 18x + 13 \). Subtract \( 18x \) from both sides: \( 3x - 20 = 13 \). Add 20 to both sides: \( 3x = 33 \). Divide by 3: \( x = 11 \).

Step3: Find \( KM \)

Substitute \( x = 11 \) into \( KM = 18x + 13 \): \( KM = 18(11) + 13 = 198 + 13 = 211 \).

Answer:

211