If $JM = 5x - 8$ And $LM = 2x - 6$, Which Expression Represents $JL$?A. $3x - 2$ B. $3x - 14$ C. $7x - 2$ D. $7x - 14$

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Understanding the Problem

In this problem, we are given two expressions representing the lengths of segments JM and LM in a geometric figure. We are asked to find the expression that represents the length of segment JL. To solve this problem, we need to use the given expressions to find the length of JL.

Given Expressions

  • JM=5x−8JM = 5x - 8
  • LM=2x−6LM = 2x - 6

Finding JL

To find the length of JL, we can use the fact that the sum of the lengths of segments JM and LM is equal to the length of JL. Mathematically, this can be represented as:

JM+LM=JLJM + LM = JL

Substituting the given expressions for JM and LM, we get:

(5x−8)+(2x−6)=JL(5x - 8) + (2x - 6) = JL

Simplifying the Expression

To simplify the expression, we can combine like terms:

5x+2x−8−6=JL5x + 2x - 8 - 6 = JL

This simplifies to:

7x−14=JL7x - 14 = JL

Conclusion

Therefore, the expression that represents JL is 7x−147x - 14. This is the correct answer.

Comparison with Options

Let's compare our answer with the options given:

  • A. 3x−23x - 2
  • B. 3x−143x - 14
  • C. 7x−27x - 2
  • D. 7x−147x - 14

Our answer, 7x−147x - 14, matches option D. Therefore, the correct answer is:

The Final Answer

D. 7x−147x - 14

Why is this the Correct Answer?

This is the correct answer because it is the result of simplifying the expression (5x−8)+(2x−6)(5x - 8) + (2x - 6), which represents the sum of the lengths of segments JM and LM. This sum is equal to the length of JL, which is what we are trying to find.

What is the Importance of this Problem?

This problem is important because it illustrates the concept of combining like terms in algebra. It also shows how to use given expressions to find the length of a segment in a geometric figure.

How to Apply this Concept in Real-Life Situations

This concept can be applied in real-life situations where you need to find the length of a segment in a geometric figure. For example, in architecture, you may need to find the length of a segment to determine the dimensions of a building. In engineering, you may need to find the length of a segment to determine the dimensions of a machine part.

Common Mistakes to Avoid

When solving this problem, some common mistakes to avoid include:

  • Not combining like terms correctly
  • Not using the correct expressions for JM and LM
  • Not simplifying the expression correctly

Tips for Solving Similar Problems

To solve similar problems, follow these tips:

  • Read the problem carefully and understand what is being asked
  • Use the given expressions to find the length of the segment
  • Combine like terms correctly
  • Simplify the expression correctly

Conclusion

Frequently Asked Questions

Q: What is the formula for finding JL?

A: The formula for finding JL is JM+LM=JLJM + LM = JL. This means that the sum of the lengths of segments JM and LM is equal to the length of JL.

Q: How do I combine like terms in the expression?

A: To combine like terms, you need to add or subtract the coefficients of the same variables. In this case, you need to add the coefficients of x and subtract the constants.

Q: What is the correct answer for JL?

A: The correct answer for JL is 7x−147x - 14. This is the result of simplifying the expression (5x−8)+(2x−6)(5x - 8) + (2x - 6), which represents the sum of the lengths of segments JM and LM.

Q: Why is option D the correct answer?

A: Option D is the correct answer because it is the result of simplifying the expression (5x−8)+(2x−6)(5x - 8) + (2x - 6), which represents the sum of the lengths of segments JM and LM. This sum is equal to the length of JL, which is what we are trying to find.

Q: How do I apply this concept in real-life situations?

A: This concept can be applied in real-life situations where you need to find the length of a segment in a geometric figure. For example, in architecture, you may need to find the length of a segment to determine the dimensions of a building. In engineering, you may need to find the length of a segment to determine the dimensions of a machine part.

Q: What are some common mistakes to avoid when solving this problem?

A: Some common mistakes to avoid when solving this problem include:

  • Not combining like terms correctly
  • Not using the correct expressions for JM and LM
  • Not simplifying the expression correctly

Q: How do I simplify the expression correctly?

A: To simplify the expression correctly, you need to combine like terms and follow the order of operations (PEMDAS). In this case, you need to add the coefficients of x and subtract the constants.

Q: What are some tips for solving similar problems?

A: Some tips for solving similar problems include:

  • Read the problem carefully and understand what is being asked
  • Use the given expressions to find the length of the segment
  • Combine like terms correctly
  • Simplify the expression correctly

Q: Can I use this concept to solve other problems?

A: Yes, you can use this concept to solve other problems that involve finding the length of a segment in a geometric figure. Just remember to follow the same steps and use the correct expressions.

Q: How do I know if I have the correct answer?

A: You can check if you have the correct answer by plugging in values for x and seeing if the expression makes sense. You can also use a calculator to check if the expression is equal to the correct answer.

Q: What if I get stuck on a problem?

A: If you get stuck on a problem, try breaking it down into smaller steps and solving each step separately. You can also ask for help from a teacher or tutor.

Conclusion

In conclusion, solving for JL in a geometric expression involves using the given expressions to find the length of the segment, combining like terms correctly, and simplifying the expression correctly. By following these steps and using the correct expressions, you can find the correct answer and apply this concept in real-life situations.