To solve for the expression that represents \( JL \), we need to combine the expressions for \( JM \) and \( LM \).
Given:
[tex]\[ JM = 5x - 8 \][/tex]
[tex]\[ LM = 2x - 6 \][/tex]
Since \( JL \) is the sum of \( JM \) and \( LM \), we can write:
[tex]\[ JL = JM + LM \][/tex]
Now, substituting the given expressions for \( JM \) and \( LM \):
[tex]\[ JL = (5x - 8) + (2x - 6) \][/tex]
Next, let's combine the like terms:
1. Add the \( x \) terms:
[tex]\[ 5x + 2x = 7x \][/tex]
2. Add the constant terms:
[tex]\[ -8 + (-6) = -14 \][/tex]
Thus, the combined expression is:
[tex]\[ JL = 7x - 14 \][/tex]
Therefore, the correct expression that represents \( JL \) is \( 7x - 14 \), which corresponds to the fourth option.
So, the correct choice is:
[tex]\[ \boxed{7x - 14} \][/tex]
