To determine which expression represents [tex]\(JL\)[/tex], let's follow these steps:
1. Identify the given expressions for [tex]\(JM\)[/tex] and [tex]\(LM\)[/tex]:
- [tex]\(JM = 5x - 8\)[/tex]
- [tex]\(LM = 2x - 6\)[/tex]
2. Find the expression for [tex]\(JL\)[/tex] by adding [tex]\(JM\)[/tex] and [tex]\(LM\)[/tex]:
[tex]\[
JL = JM + LM = (5x - 8) + (2x - 6)
\][/tex]
3. Combine like terms:
- Combine the [tex]\(x\)[/tex] terms: [tex]\(5x + 2x = 7x\)[/tex]
- Combine the constant terms: [tex]\(-8 - 6 = -14\)[/tex]
4. Write the simplified expression for [tex]\(JL\)[/tex]:
[tex]\[
JL = 7x - 14
\][/tex]
5. Compare the simplified expression with the given options:
- [tex]\(3x - 2\)[/tex]
- [tex]\(3x - 14\)[/tex]
- [tex]\(7x - 2\)[/tex]
- [tex]\(7x - 14\)[/tex]
6. Identify the matching expression:
- The expression [tex]\(7x - 14\)[/tex] matches one of the given options.
Therefore, the expression that represents [tex]\(JL\)[/tex] is [tex]\(7x - 14\)[/tex].
So, the correct option is:
[tex]\[ \boxed{7x - 14} \][/tex]
