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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
Certainly! To solve the problem, we need to determine the value of [tex]\( JL \)[/tex] based on the given expressions for [tex]\( JM \)[/tex] and [tex]\( LM \)[/tex]. Follow these steps:

1. Given expressions:
[tex]\[ JM = 5x - 8 \][/tex]
[tex]\[ LM = 2x - 6 \][/tex]

2. Determine [tex]\( JL \)[/tex]:
Since [tex]\( JL \)[/tex] is the sum of [tex]\( JM \)[/tex] and [tex]\( LM \)[/tex], we add the two expressions together:
[tex]\[ JL = JM + LM \][/tex]

3. Add the expressions:
[tex]\[ JL = (5x - 8) + (2x - 6) \][/tex]

4. Combine like terms:
- Combine the [tex]\( x \)[/tex]-terms:
[tex]\[ 5x + 2x = 7x \][/tex]
- Combine the constant terms:
[tex]\[ -8 - 6 = -14 \][/tex]

5. Write the simplified expression for [tex]\( JL \)[/tex]:
[tex]\[ JL = 7x - 14 \][/tex]

6. Identify the matching expression:
Given the potential options:
- [tex]\( 3x - 2 \)[/tex]
- [tex]\( 3x - 14 \)[/tex]
- [tex]\( 7x - 2 \)[/tex]
- [tex]\( 7x - 14 \)[/tex]

We see that the simplified expression [tex]\( 7x - 14 \)[/tex] matches one of the given choices.

Conclusion:
The expression that represents [tex]\( JL \)[/tex] is
[tex]\[ 7x - 14 \][/tex]

Therefore, the correct answer is:
[tex]\[ \boxed{7x - 14} \][/tex]

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