To determine the expression representing [tex]\( JL \)[/tex], let's consider the given information:
- [tex]\( JM = 5x - 8 \)[/tex]
- [tex]\( LM = 2x - 6 \)[/tex]
The length [tex]\( JL \)[/tex] is the sum of [tex]\( JM \)[/tex] and [tex]\( LM \)[/tex]. So, we need to add the two expressions:
[tex]\[ JL = JM + LM \][/tex]
Substitute the given expressions for [tex]\( JM \)[/tex] and [tex]\( LM \)[/tex]:
[tex]\[ JL = (5x - 8) + (2x - 6) \][/tex]
Now, combine like terms:
1. Combine the [tex]\( x \)[/tex]-terms:
[tex]\[ 5x + 2x = 7x \][/tex]
2. Combine the constant terms:
[tex]\[ -8 - 6 = -14 \][/tex]
Putting it all together, we get the expression:
[tex]\[ JL = 7x - 14 \][/tex]
Thus, the correct expression representing [tex]\( JL \)[/tex] is:
[tex]\[ 7x - 14 \][/tex]
Among the given options, the expression [tex]\( 7x - 14 \)[/tex] corresponds to the fourth option. Therefore, the correct answer is:
[tex]\[ \boxed{7x - 14} \][/tex]
