To determine the expression for [tex]\(JL\)[/tex] given [tex]\(JM = 5x - 8\)[/tex] and [tex]\(LM = 2x - 6\)[/tex], we need to add the expressions for [tex]\(JM\)[/tex] and [tex]\(LM\)[/tex].
Here is the step-by-step process:
1. Start with the given expressions:
[tex]\[
JM = 5x - 8
\][/tex]
[tex]\[
LM = 2x - 6
\][/tex]
2. Add the two expressions together to find [tex]\(JL\)[/tex]:
[tex]\[
JL = JM + LM
\][/tex]
[tex]\[
JL = (5x - 8) + (2x - 6)
\][/tex]
3. Combine like terms:
[tex]\[
JL = 5x + 2x - 8 - 6
\][/tex]
[tex]\[
JL = 7x - 14
\][/tex]
Hence, the expression that represents [tex]\(JL\)[/tex] is:
[tex]\[
7x - 14
\][/tex]
Therefore, the correct option is:
[tex]\[
\boxed{7 x - 14}
\][/tex]
