To determine the expression for [tex]\( JL \)[/tex] given that [tex]\( JM = 5x - 8 \)[/tex] and [tex]\( LM = 2x - 6 \)[/tex], we need to find the sum of [tex]\( JM \)[/tex] and [tex]\( LM \)[/tex].
Here's a step-by-step solution:
1. Write down 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]
Substitute the given expressions:
[tex]\[
JL = (5x - 8) + (2x - 6)
\][/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]
Therefore, the expression that represents [tex]\( JL \)[/tex] is [tex]\( 7x - 14 \)[/tex].
The correct answer is:
[tex]\[
\boxed{7x - 14}
\][/tex]
