Question

if (kl = x + 10), (lm = 2x), and (km = 4x + 2), what is (lm)? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set up equation based on segment - addition postulate

Since $KL + LM=KM$, we substitute the given expressions: $(x + 10)+2x=4x + 2$.

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

$x+2x + 10=4x + 2$, which simplifies to $3x+10 = 4x + 2$.

Step3: Solve for $x$

Subtract $3x$ from both sides: $10=x + 2$. Then subtract 2 from both sides to get $x = 8$.

Step4: Find the value of $LM$

Since $LM = 2x$, substitute $x = 8$ into the expression for $LM$. So $LM=2\times8=16$.

Answer:

16