Question

if $kl = 2x + 16$, $lm = 15x$, and $km = 16x + 17$, what is $lm$? 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: $16x + 17=(2x + 16)+15x$.

Step2: Simplify the right - hand side

Combine like terms on the right - hand side: $(2x + 16)+15x=2x+15x + 16=17x + 16$. So, $16x + 17=17x + 16$.

Step3: Solve for x

Subtract $16x$ from both sides: $16x+17-16x=17x + 16-16x$, which gives $17=x + 16$. Then subtract 16 from both sides: $x=17 - 16=1$.

Step4: Find the value of LM

Since $LM = 15x$ and $x = 1$, then $LM=15\times1 = 15$.

Answer:

15