Point K is on line segment JL. given JL = 4x+2, KL = 5x - 6, and JK = 3x, determine the numerical length of JK

To solve for the length of \( JK \), we need to use the fact that \( JK + KL = JL \), since \( K \) is a point on the line segment \( JL \).

Given:
\[
JL = 4x + 2, \quad KL = 5x - 6, \quad JK = 3x
\]

We can set up the equation:
\[
JK + KL = JL
\]
Substituting the given expressions:
\[
3x + (5x - 6) = 4x + 2
\]

Now, simplify the equation:
\[
3x + 5x - 6 = 4x + 2
\]
\[
8x - 6 = 4x + 2
\]

Next, move all terms involving \( x \) to one side and the constant terms to the other side:
\[
8x - 4x = 2 + 6
\]
\[
4x = 8
\]

Solve for \( x \):
\[
x = 2
\]

Now that we have \( x = 2 \), we can find the numerical length of \( JK \) by substituting \( x \) back into the expression for \( JK \):
\[
JK = 3x = 3(2) = 6
\]

Thus, the numerical length of \( JK \) is \( \boxed{6} \).

Would you like to know more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would the result change if the expressions for \( JL \) and \( KL \) were different?
2. What if point \( K \) were not on the segment \( JL \)? How would that affect the calculations?
3. How can you verify that your solution is correct?
4. What if \( JK \) and \( KL \) had overlapping or shared lengths?
5. How can this problem be extended to three dimensions?

**Tip:** Always double-check the arrangement of your algebraic equation and your solution step-by-step to avoid mistakes.

Point K is on line segment JL. Given JL = 4x+2, KL = 5x - 6, and JK = 3x, determine the numerical length of JK.

Determine the length of JK using algebraic expressions in the context of segment addition. Given JL = 4x+2, KL = 5x - 6, and JK = 3x, learn the step-by-step process to find the value of x and the length of JK. 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