Question

if (lm = 3x), (mn=x + 1), and (ln = 9), what is (lm)?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set up the equation

Since $LN=LM + MN$, we have $3x+(x + 1)=9$.

Step2: Combine like - terms

Combining the $x$ terms on the left - hand side gives $4x+1 = 9$.

Step3: Isolate the variable term

Subtract 1 from both sides: $4x=9 - 1$, so $4x=8$.

Step4: Solve for $x$

Divide both sides by 4: $x=\frac{8}{4}=2$.

Step5: Find $LM$

Since $LM = 3x$, substitute $x = 2$ into the expression for $LM$. So $LM=3\times2 = 6$.

Answer:

6