To determine which expression represents [tex]\( JL \)[/tex], we need to add the expressions for [tex]\( JM \)[/tex] and [tex]\( LM \)[/tex].
Given:
[tex]\[ JM = 5x - 8 \][/tex]
[tex]\[ LM = 2x - 6 \][/tex]
To find [tex]\( JL \)[/tex], we add [tex]\( JM \)[/tex] and [tex]\( LM \)[/tex]:
[tex]\[ JL = (5x - 8) + (2x - 6) \][/tex]
Let's add the two expressions step-by-step.
1. Combine the [tex]\( x \)[/tex]-terms:
[tex]\[ 5x + 2x = 7x \][/tex]
2. Combine the constant terms:
[tex]\[ -8 - 6 = -14 \][/tex]
Hence, the expression for [tex]\( JL \)[/tex] is:
[tex]\[ JL = 7x - 14 \][/tex]
Now, we need to find this expression among the given answer choices:
1. [tex]\( 3x - 2 \)[/tex]
2. [tex]\( 3x - 14 \)[/tex]
3. [tex]\( 7x - 2 \)[/tex]
4. [tex]\( 7x - 14 \)[/tex]
The correct expression for [tex]\( JL \)[/tex] is [tex]\( 7x - 14 \)[/tex], which matches the fourth option.
Therefore, the correct answer is:
[tex]\[ 7x - 14 \][/tex]
Among the given options, this is option number 4.
