13. If \( K \) is the midpoint of \( \overline{J L}, J K=8 x+11 \) and \( K L=14 x-1 \), find \( J L \).

To find the length of \( J L \), we start by using the information given about the segments \( J K \) and \( K L \). Since \( K \) is the midpoint of \( \overline{J L} \), we know that: \[ J K = K L \] We are given the expressions for \( J K \) and \( K L \): \[ J K = 8x + 11 \] \[ K L = 14x - 1 \] Setting these two expressions equal to each other gives us: \[ 8x + 11 = 14x - 1 \] Now, we will solve for \( x \). First, we can rearrange the equation by moving all terms involving \( x \) to one side and constant terms to the other side: \[ 11 + 1 = 14x - 8x \] This simplifies to: \[ 12 = 6x \] Now, divide both sides by 6: \[ x = 2 \] Next, we substitute \( x = 2 \) back into either expression for \( J K \) or \( K L \) to find the length of \( J K \) (and \( K L \), since they are equal). Using \( J K \): \[ J K = 8(2) + 11 = 16 + 11 = 27 \] Now that we have \( J K \) and \( K L \), we can find the total length of \( J L \): \[ J L = J K + K L = 27 + 27 = 54 \] Thus, the length of \( J L \) is: \[ \boxed{54} \]