Question

1. k•---7---•l---2x - 6---•m

↔-----------x + 9-----------↔ x = ______
7 + (2x - 6 = x + 9
-8 + 2x = x + 9
-1x -1x

Explanation:

Step1: Set up the equation

From the segment addition postulate, \( K L + L M = K M \). So we have \( 7+(2x - 6)=x + 9 \).

Step2: Simplify the left side

Simplify \( 7+(2x - 6) \) to get \( 2x+1 \). So the equation becomes \( 2x + 1=x + 9 \).

Step3: Solve for x

Subtract \( x \) from both sides: \( 2x - x+1=x - x + 9 \), which simplifies to \( x+1 = 9 \). Then subtract 1 from both sides: \( x+1 - 1=9 - 1 \), so \( x = 8 \).

Answer:

\( 8 \)