https://file.aiquickdraw.com/mathbot/file/1729869975624g1tl3th2.jpg

The problem asks to find the value of \( JK \), given that:

- \( K \) is the midpoint of \( \overline{JL} \).
- \( JK = 10x \) 
- \( JL = 16x + 7 \)

Since \( K \) is the midpoint, \( JK \) is half of \( JL \). Therefore, we can set up the following equation:

\[
JK = \frac{JL}{2}
\]

Now, substitute \( JL = 16x + 7 \) into this equation:

\[
JK = \frac{16x + 7}{2}
\]

We also know that \( JK = 10x \), so we set the two expressions for \( JK \) equal to each other:

\[
10x = \frac{16x + 7}{2}
\]

To solve for \( x \), first multiply both sides of the equation by 2 to eliminate the denominator:

\[
20x = 16x + 7
\]

Now, subtract \( 16x \) from both sides:

\[
4x = 7
\]

Solve for \( x \):

\[
x = \frac{7}{4}
\]

Now that we have \( x = \frac{7}{4} \), substitute this value back into the expression for \( JK \):

\[
JK = 10x = 10 \times \frac{7}{4} = \frac{70}{4} = 17\frac{1}{2}
\]

Thus, the value of \( JK \) is \( 17 \frac{1}{2} \), or \( 17.5 \).

Would you like further clarification or details on this solution?

Here are five related questions for practice:
1. What is the length of \( KL \), given that \( K \) is the midpoint?
2. How would the solution change if \( K \) were not the midpoint?
3. What is the total length of \( \overline{JL} \)?
4. How do you solve for \( x \) when dealing with fractional equations?
5. How does the midpoint property affect other types of geometric problems?

**Tip:** Always check your solution by substituting back the value of the variable to ensure it satisfies the original equation.

K is the midpoint of JL. If JK = 10x and JL = 16x + 7, what is JK?

Learn how to solve for JK when K is the midpoint of JL, and you are given linear expressions for JK and JL. This problem explores key algebraic and geometric concepts such as the midpoint theorem and solving linear equations. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation