Question

k is the midpoint of (overline{jl}). if (kl = x + 5) and (jl = 7x + 5), what is (jl)? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use midpoint property

Since \( K \) is the midpoint of \( \overline{JL} \), then \( JL = 2 \times KL \). So we have the equation \( 7x + 5 = 2(x + 5) \).

Step2: Solve for \( x \)

Expand the right side: \( 7x + 5 = 2x + 10 \).
Subtract \( 2x \) from both sides: \( 7x - 2x + 5 = 10 \), which simplifies to \( 5x + 5 = 10 \).
Subtract 5 from both sides: \( 5x = 10 - 5 = 5 \).
Divide both sides by 5: \( x = \frac{5}{5} = 1 \).

Step3: Find \( JL \)

Substitute \( x = 1 \) into \( JL = 7x + 5 \). So \( JL = 7(1) + 5 = 7 + 5 = 12 \).

Answer:

12