Let's solve the problem step-by-step.
1. Identify the expressions for JM and LM:
Given:
[tex]\[
JM = 5x - 8
\][/tex]
[tex]\[
LM = 2x - 6
\][/tex]
2. Determine the expression for JL by adding JM and LM:
[tex]\[
JL = JM + LM
\][/tex]
Substituting the given expressions:
[tex]\[
JL = (5x - 8) + (2x - 6)
\][/tex]
3. Combine the like terms:
- Combine the [tex]\(x\)[/tex] terms: [tex]\(5x + 2x\)[/tex]
- Combine the constant terms: [tex]\(-8 - 6\)[/tex]
Thus,
[tex]\[
JL = 5x + 2x - 8 - 6
\][/tex]
Simplifying this:
[tex]\[
JL = 7x - 14
\][/tex]
4. Compare with the given options:
Let's list the options again:
[tex]\[
\text{(A) } 3x - 2
\][/tex]
[tex]\[
\text{(B) } 3x - 14
\][/tex]
[tex]\[
\text{(C) } 7x - 2
\][/tex]
[tex]\[
\text{(D) } 7x - 14
\][/tex]
The expression we found for JL is [tex]\(7x - 14\)[/tex].
5. Determine the correct choice:
By comparing [tex]\(JL = 7x - 14\)[/tex] with the options, it's clear that the correct option is:
[tex]\[
\boxed{7x - 14}
\][/tex]
Therefore, the expression that represents [tex]\( JL \)[/tex] is:
[tex]\[
\boxed{7x - 14}
\][/tex]
This corresponds to option D. Therefore, the answer is:
[tex]\[
\boxed{4}
\][/tex]
