Question

if (kl = 3x), (lm=x + 5), and (km = 9), what is (lm)? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment - addition postulate

Since $KM=KL + LM$, we have the equation $3x+(x + 5)=9$.

Step2: Combine like - terms

Combine the $x$ terms on the left - hand side: $3x+x+5 = 9$, which simplifies to $4x+5 = 9$.

Step3: Isolate the variable term

Subtract 5 from both sides of the equation: $4x+5−5=9 - 5$, resulting in $4x=4$.

Step4: Solve for $x$

Divide both sides by 4: $\frac{4x}{4}=\frac{4}{4}$, so $x = 1$.

Step5: Find the value of $LM$

Substitute $x = 1$ into the expression for $LM$. Since $LM=x + 5$, then $LM=1+5=6$.

Answer:

6