To find the expression for [tex]\( JL \)[/tex], given the expressions for [tex]\( JM \)[/tex] and [tex]\( LM \)[/tex]:
[tex]\[ JM = 5x - 8 \][/tex]
[tex]\[ LM = 2x - 6 \][/tex]
we need to determine the relationship between these segments.
The problem infers that [tex]\( JL \)[/tex] is the sum of [tex]\( JM \)[/tex] and [tex]\( LM \)[/tex]:
[tex]\[ JL = JM + LM \][/tex]
Substitute the given expressions for [tex]\( JM \)[/tex] and [tex]\( LM \)[/tex]:
[tex]\[ JL = (5x - 8) + (2x - 6) \][/tex]
Combine like terms:
[tex]\[ JL = 5x + 2x - 8 - 6 \][/tex]
[tex]\[ JL = 7x - 14 \][/tex]
Therefore, the expression that represents [tex]\( JL \)[/tex] is:
[tex]\[ 7x - 14 \][/tex]
Hence, the correct option is:
[tex]\[ 7x - 14 \][/tex]
