Question

if kl = 11x, lm = 5x + 2, and km = 18x - 12, what is kl? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment - addition postulate

Since $KL + LM=KM$, we substitute the given expressions: $11x+(5x + 2)=18x-12$.

Step2: Combine like - terms on the left - hand side

$11x+5x + 2=16x + 2$. So, the equation becomes $16x+2 = 18x-12$.

Step3: Isolate the variable $x$

Subtract $16x$ from both sides: $16x+2-16x=18x - 12-16x$, which simplifies to $2 = 2x-12$. Then add 12 to both sides: $2 + 12=2x-12 + 12$, resulting in $14 = 2x$. Divide both sides by 2: $\frac{14}{2}=\frac{2x}{2}$, so $x = 7$.

Step4: Find the value of $KL$

Since $KL = 11x$, substitute $x = 7$ into the expression for $KL$. Then $KL=11\times7 = 77$.

Answer:

77