Question

if kl = 10x - 7, lm = x + 6, and km = 10, what is kl?
diagram of k---l---m with kl=10x-7, lm=x+6, km=10
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set up the equation

From the segment addition postulate, \( KL + LM = KM \). Substitute the given expressions: \( (10x - 7) + (x + 6) = 10 \).

Step2: Simplify the left side

Combine like terms: \( 10x + x - 7 + 6 = 10 \) → \( 11x - 1 = 10 \).

Step3: Solve for \( x \)

Add 1 to both sides: \( 11x = 10 + 1 \) → \( 11x = 11 \). Divide by 11: \( x = \frac{11}{11} = 1 \).

Step4: Find \( KL \)

Substitute \( x = 1 \) into \( KL = 10x - 7 \): \( KL = 10(1) - 7 = 10 - 7 = 3 \).

Answer:

3