Question

if kl = 8x, lm = 16x − 6, and km = 18, what is kl? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set up the equation

From the line segment, we know that \( KL + LM = KM \). Substituting the given expressions, we get \( 8x + (16x - 6) = 18 \).

Step2: Simplify the left side

Combine like terms: \( 8x + 16x - 6 = 24x - 6 \). So the equation becomes \( 24x - 6 = 18 \).

Step3: Solve for x

Add 6 to both sides: \( 24x - 6 + 6 = 18 + 6 \), which simplifies to \( 24x = 24 \). Then divide both sides by 24: \( x = \frac{24}{24} = 1 \).

Step4: Find KL

Since \( KL = 8x \) and \( x = 1 \), substitute x into the expression: \( KL = 8\times1 = 8 \).

Answer:

8