Question

m is a point on segment (overline{ln}). if (lm = 5x - 3), (mn = x + 8), and (ln = 17), what is (mn)? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

Since \( M \) is on \( \overline{LN} \), we have \( LM + MN = LN \). Substituting the given expressions: \( (5x - 3) + (x + 8) = 17 \).

Step2: Simplify and solve for \( x \)

Combine like terms: \( 5x - 3 + x + 8 = 17 \) becomes \( 6x + 5 = 17 \). Subtract 5 from both sides: \( 6x = 17 - 5 = 12 \). Then divide by 6: \( x = \frac{12}{6} = 2 \).

Step3: Find \( MN \)

Substitute \( x = 2 \) into \( MN = x + 8 \): \( MN = 2 + 8 = 10 \).

Answer:

\( 10 \)