Question

on a line segment, l is between k and m. if kl = 9x - 13, lm = 12x - 17, and km = 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 $L$ is between $K$ and $M$, $KL + LM=KM$. Substitute the given expressions: $(9x - 13)+(12x - 17)=12$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms: $9x+12x-13 - 17 = 12$, which simplifies to $21x-30 = 12$.

Step3: Isolate the variable term

Add 30 to both sides of the equation: $21x-30 + 30=12 + 30$, resulting in $21x=42$.

Step4: Solve for $x$

Divide both sides by 21: $x=\frac{42}{21}=2$.

Step5: Find the value of $KL$

Substitute $x = 2$ into the expression for $KL$: $KL=9x - 13=9\times2-13$.
$KL = 18 - 13=5$.

Answer:

5