If $JM = 5x - 8$ And $LM = 2x - 6$, Which Expression Represents \$JL$[/tex\]?A. $3x - 2$ B. $3x - 14$ C. \$7x - 2$[/tex\] D. $7x - 14$
Understanding the Problem
To find the expression that represents $, we need to understand the given information and how it relates to the unknown value. The problem provides two equations: $JM = 5x - 8$ and $LM = 2x - 6$. These equations represent the lengths of two line segments, $JM$ and $LM$, in terms of the variable $x$. Our goal is to find the expression that represents the length of the line segment $JL$.
Finding the Expression for JL
To find the expression for $JL$, we need to use the given equations and apply some algebraic manipulations. We can start by adding the two equations together:
Simplifying the equation, we get:
Understanding the Concept of Addition of Line Segments
When we add two line segments, we are essentially finding the total length of the combined segments. In this case, we are adding $JM$ and $LM$ to find the total length of the line segment $JL$. However, we need to be careful when adding line segments, as the order of addition can affect the result.
Finding the Correct Expression for JL
Since we are adding $JM$ and $LM$ to find the total length of $JL$, we need to make sure that we are adding the correct segments. In this case, we are adding $JM$ and $LM$, which means that we are adding the segments in the correct order.
However, we need to consider the fact that the order of addition can affect the result. In this case, we are adding the segments in the order $JM$ and $LM$, which means that we are adding the segments in the correct order.
Conclusion
Based on the given information and the algebraic manipulations, we can conclude that the expression that represents $JL$ is:
This expression represents the total length of the line segment $JL$, which is the sum of the lengths of the line segments $JM$ and $LM$.
Answer
The correct answer is:
D. $7x - 14$
Explanation
The correct answer is D. $7x - 14$ because it represents the total length of the line segment $JL$, which is the sum of the lengths of the line segments $JM$ and $LM$.
Tips and Tricks
When working with line segments, it's essential to consider the order of addition. In this case, we added $JM$ and $LM$ to find the total length of $JL$. However, we need to make sure that we are adding the correct segments in the correct order.
Real-World Applications
Understanding the concept of addition of line segments is crucial in various real-world applications, such as:
- Calculating the total length of a road or a path
- Finding the distance between two points on a map
- Calculating the length of a wire or a cable
Practice Problems
To practice working with line segments, try the following problems:
- Find the expression that represents the length of the line segment $AB$, given that $AB = 3x + 2$ and $BC = 2x - 4$.
- Find the expression that represents the length of the line segment $CD$, given that $CD = 5x - 3$ and $DA = 2x + 1$.
Conclusion
In conclusion, the expression that represents $JL$ is $7x - 14$. This expression represents the total length of the line segment $JL$, which is the sum of the lengths of the line segments $JM$ and $LM$.
Frequently Asked Questions
Q: What is the difference between adding line segments and adding numbers?
A: When adding line segments, we are finding the total length of the combined segments. However, when adding numbers, we are simply finding the sum of the values. In the case of line segments, we need to consider the order of addition and make sure that we are adding the correct segments.
Q: How do I determine the correct order of addition when working with line segments?
A: To determine the correct order of addition, we need to consider the direction of the line segments. When adding line segments, we need to make sure that we are adding the segments in the correct order to get the total length.
Q: What is the significance of the variable x in the given equations?
A: The variable x represents a value that is used to calculate the lengths of the line segments. In the given equations, x is used to calculate the lengths of the line segments JM and LM.
Q: How do I simplify the equation JM + LM = (5x - 8) + (2x - 6)?
A: To simplify the equation, we need to combine like terms. In this case, we can combine the x terms and the constant terms separately. This will give us the simplified equation 7x - 14.
Q: What is the relationship between the given equations and the expression for JL?
A: The given equations represent the lengths of the line segments JM and LM, and the expression for JL is the sum of these two lengths. Therefore, the expression for JL is equal to the sum of the given equations.
Q: How do I determine the correct expression for JL?
A: To determine the correct expression for JL, we need to consider the given equations and the relationship between the line segments. In this case, we can add the given equations to find the expression for JL.
Q: What is the significance of the expression 7x - 14 in the context of the problem?
A: The expression 7x - 14 represents the total length of the line segment JL, which is the sum of the lengths of the line segments JM and LM.
Q: How do I apply the concept of addition of line segments to real-world problems?
A: To apply the concept of addition of line segments to real-world problems, we need to consider the lengths of the line segments and the order of addition. We can use this concept to calculate the total length of a road or a path, find the distance between two points on a map, or calculate the length of a wire or a cable.
Q: What are some common mistakes to avoid when working with line segments?
A: Some common mistakes to avoid when working with line segments include:
- Adding line segments in the wrong order
- Failing to consider the direction of the line segments
- Not simplifying the equation correctly
- Not considering the relationship between the line segments
Tips and Tricks
- When working with line segments, make sure to consider the order of addition and the direction of the line segments.
- Simplify the equation correctly by combining like terms.
- Consider the relationship between the line segments and the given equations.
- Apply the concept of addition of line segments to real-world problems.
Practice Problems
- Find the expression that represents the length of the line segment AB, given that AB = 3x + 2 and BC = 2x - 4.
- Find the expression that represents the length of the line segment CD, given that CD = 5x - 3 and DA = 2x + 1.
Conclusion
In conclusion, the expression that represents JL is 7x - 14. This expression represents the total length of the line segment JL, which is the sum of the lengths of the line segments JM and LM. By understanding the concept of addition of line segments and applying it to real-world problems, we can solve a variety of problems involving line segments.