Alright, let's solve the problem step-by-step.
We have two segments, [tex]\( JM \)[/tex] and [tex]\( LM \)[/tex], which are parts of the line segment [tex]\( JL \)[/tex]. The given expressions are:
[tex]\[ JM = 5x - 8 \][/tex]
[tex]\[ LM = 2x - 6 \][/tex]
To find the expression for [tex]\( JL \)[/tex], we need to add the lengths of [tex]\( JM \)[/tex] and [tex]\( LM \)[/tex].
Combining [tex]\( JM \)[/tex] and [tex]\( LM \)[/tex], we get:
[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, let's combine the like terms. First, combine the terms containing [tex]\( x \)[/tex]:
[tex]\[ JL = 5x + 2x \][/tex]
Next, combine the constant terms:
[tex]\[ JL = -8 - 6 \][/tex]
So we have:
[tex]\[ JL = 7x - 14 \][/tex]
Therefore, the expression that represents [tex]\( JL \)[/tex] is:
[tex]\[ 7x - 14 \][/tex]
Among the given choices, the correct answer is:
[tex]\[ 7x - 14 \][/tex]
So, the final answer is:
[tex]\[ \boxed{7x - 14} \][/tex]
