To solve for $JK$, we need to use the fact that the line $\ell$ is a straight line, which implies that the sum of the distances on either side of point $M$ should be equal to the entire segment $JK$. The expressions for the distances are given as follows:

• $JM = 3x + 15$
• $MK = 8x + 25$

Since $JK$ is a straight line, we have the equation:

$JM + MK = JK$

Substituting the expressions for $JM$ and $MK$, we get:

$(3x + 15) + (8x + 25) = JK$

Simplifying the left-hand side:

$3x + 15 + 8x + 25 = JK$

$11x + 40 = JK$

Now, to find the value of $JK$, we would need to determine $x$. However, if no further conditions are provided, $JK$ will remain expressed as $11x + 40$.

Do you have additional information for solving $x$, or should we leave $JK$ in terms of $x$? Let me know if you want further details on any part of this!

Related Questions:

1. How do we find $x$ if additional constraints are provided?
2. What are the properties of line segments and how are they applied in geometry problems?
3. How can we check if two segments are congruent using algebraic expressions?
4. What is the concept of partitioning a line in terms of segments?
5. How do parallel lines affect the relationships of angles and distances?

Tip:

Always check if the problem contains geometric properties like congruence, parallelism, or additional relationships that can help determine unknown variables.