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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]

Sagot :

GinnyAnswer
To determine which expression represents [tex]\(JL\)[/tex], let's follow these steps:

1. Identify the given expressions for [tex]\(JM\)[/tex] and [tex]\(LM\)[/tex]:
- [tex]\(JM = 5x - 8\)[/tex]
- [tex]\(LM = 2x - 6\)[/tex]

2. Find the expression for [tex]\(JL\)[/tex] by adding [tex]\(JM\)[/tex] and [tex]\(LM\)[/tex]:
[tex]\[ JL = JM + LM = (5x - 8) + (2x - 6) \][/tex]

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

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

5. Compare the simplified expression with the given options:
- [tex]\(3x - 2\)[/tex]
- [tex]\(3x - 14\)[/tex]
- [tex]\(7x - 2\)[/tex]
- [tex]\(7x - 14\)[/tex]

6. Identify the matching expression:
- The expression [tex]\(7x - 14\)[/tex] matches one of the given options.

Therefore, the expression that represents [tex]\(JL\)[/tex] is [tex]\(7x - 14\)[/tex].

So, the correct option is:

[tex]\[ \boxed{7x - 14} \][/tex]
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