Question

on a line segment, m is between l and n. if lm = 11, mn = x - 7, and ln = 2x - 7, what is mn? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment - addition postulate

Since $M$ is between $L$ and $N$, we have $LM + MN=LN$. Substitute the given expressions: $11+(x - 7)=2x - 7$.

Step2: Simplify the left - hand side

Combine like terms on the left - hand side: $11+x - 7=x + 4$. So the equation becomes $x + 4=2x - 7$.

Step3: Solve for $x$

Subtract $x$ from both sides: $x+4−x=2x - 7−x$, which gives $4=x - 7$. Then add 7 to both sides: $4 + 7=x-7 + 7$, so $x = 11$.

Step4: Find the length of $MN$

Substitute $x = 11$ into the expression for $MN$. Since $MN=x - 7$, then $MN=11 - 7$.

Answer:

4