Question

if kl = 2x, lm = 6x - 16, and km = 4x + 8, what is km? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

From the number line, we know that \( KL + LM = KM \). Substituting the given expressions: \( 2x+(6x - 18)=4x + 8 \).

Step2: Simplify the left side

Combine like terms: \( 2x+6x-18 = 8x - 18 \). So the equation becomes \( 8x - 18=4x + 8 \).

Step3: Solve for x

Subtract \( 4x \) from both sides: \( 8x-4x - 18=4x-4x + 8 \), which simplifies to \( 4x - 18 = 8 \). Then add 18 to both sides: \( 4x-18 + 18=8 + 18 \), so \( 4x=26 \). Divide both sides by 4: \( x=\frac{26}{4}=\frac{13}{2} \).

Step4: Find KM

Substitute \( x = \frac{13}{2} \) into the expression for \( KM \), which is \( 4x + 8 \). So \( KM=4\times\frac{13}{2}+8 \).

Step5: Simplify the expression

First, \( 4\times\frac{13}{2}=2\times13 = 26 \). Then \( 26 + 8=34 \).

Answer:

34