Question

if jm = 5x - 8 and lm = 2x - 6, which expression represents jl?
j k l m
○ 3x - 2
○ 3x - 14
○ 7x - 2
○ 7x - 14

Explanation:

Step1: Understand Segment Addition

On the line segment \( JM \), point \( L \) is between \( J \) and \( M \), so \( JL + LM = JM \). Rearranging, \( JL = JM - LM \).

Step2: Substitute Expressions

Substitute \( JM = 5x - 8 \) and \( LM = 2x - 6 \) into \( JL = JM - LM \):
\[
JL=(5x - 8)-(2x - 6)
\]

Step3: Simplify the Expression

Distribute the negative sign:
\[
JL = 5x - 8 - 2x + 6
\]
Combine like terms (\( 5x - 2x = 3x \) and \( -8 + 6 = -2 \)):
\[
JL = 3x - 2
\]

Answer:

\( 3x - 2 \) (corresponding to the first option)