Question

if $lm = 20$, $mn = x + 18$, and $ln = 4x - 7$, what is $ln$?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

From the diagram, \( LN = LM + MN \). Substitute the given expressions: \( 4x - 7 = 20 + (x + 18) \)

Step2: Simplify the equation

Simplify the right - hand side: \( 4x - 7 = x + 38 \)

Step3: Solve for x

Subtract \( x \) from both sides: \( 4x - x-7=x - x + 38\), which gives \( 3x-7 = 38 \). Then add 7 to both sides: \( 3x-7 + 7=38 + 7\), so \( 3x=45 \). Divide both sides by 3: \( x = 15 \)

Step4: Find the length of LN

Substitute \( x = 15 \) into the expression for \( LN \): \( LN=4x - 7=4\times15-7 \)
Calculate \( 4\times15 = 60 \), then \( 60-7 = 53 \)

Answer:

\( 53 \)