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If [tex]JM = 5x - 8[/tex] and [tex]LM = 2x - 6[/tex], which expression represents [tex]JL[/tex]?

A. [tex]3x - 2[/tex]
B. [tex]3x - 14[/tex]
C. [tex]7x - 2[/tex]
D. [tex]7x - 14[/tex]



Answer :

GinnyAnswer
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]

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