Certainly! To solve the problem, we need to determine the value of [tex]\( JL \)[/tex] based on the given expressions for [tex]\( JM \)[/tex] and [tex]\( LM \)[/tex]. Follow these steps:
1. Given expressions:
[tex]\[
JM = 5x - 8
\][/tex]
[tex]\[
LM = 2x - 6
\][/tex]
2. Determine [tex]\( JL \)[/tex]:
Since [tex]\( JL \)[/tex] is the sum of [tex]\( JM \)[/tex] and [tex]\( LM \)[/tex], we add the two expressions together:
[tex]\[
JL = JM + LM
\][/tex]
3. Add the expressions:
[tex]\[
JL = (5x - 8) + (2x - 6)
\][/tex]
4. Combine like terms:
- Combine the [tex]\( x \)[/tex]-terms:
[tex]\[
5x + 2x = 7x
\][/tex]
- Combine the constant terms:
[tex]\[
-8 - 6 = -14
\][/tex]
5. Write the simplified expression for [tex]\( JL \)[/tex]:
[tex]\[
JL = 7x - 14
\][/tex]
6. Identify the matching expression:
Given the potential options:
- [tex]\( 3x - 2 \)[/tex]
- [tex]\( 3x - 14 \)[/tex]
- [tex]\( 7x - 2 \)[/tex]
- [tex]\( 7x - 14 \)[/tex]
We see that the simplified expression [tex]\( 7x - 14 \)[/tex] matches one of the given choices.
Conclusion:
The expression that represents [tex]\( JL \)[/tex] is
[tex]\[ 7x - 14 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{7x - 14} \][/tex]
