Question

if (kl = 11x), (lm = 14x - 8), and (km = 19x - 2), what is (km?) simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Apply segment - addition postulate

Since $KM=KL + LM$, we substitute the given expressions: $19x - 2=11x+(14x - 8)$.

Step2: Simplify the right - hand side

$19x - 2=11x + 14x-8$, and $11x + 14x=25x$, so $19x - 2=25x-8$.

Step3: Isolate the variable terms

Subtract $19x$ from both sides: $19x-19x - 2=25x-19x - 8$, which gives $- 2=6x-8$.

Step4: Solve for $x$

Add 8 to both sides: $-2 + 8=6x-8 + 8$, so $6 = 6x$. Then divide both sides by 6: $x = 1$.

Step5: Find the value of $KM$

Substitute $x = 1$ into the expression for $KM$: $KM=19x-2=19\times1-2$.
$KM=19 - 2=17$.

Answer:

17