Question

point m lies between points l and n on ln. if ln = 12x + 16, what is the length of ln in units? 16 units 40 units 48 units 64 units

Explanation:

Step1: Use segment - addition postulate

Since point $M$ lies between $L$ and $N$ on $\overline{LN}$, we have $LM + MN=LN$. Substituting the given expressions: $(10x + 8)+(5x - 4)=12x + 16$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $10x+5x + 8-4=15x + 4$. So, $15x + 4=12x + 16$.

Step3: Solve for $x$

Subtract $12x$ from both sides: $15x-12x+4=12x - 12x+16$, which gives $3x+4 = 16$. Then subtract 4 from both sides: $3x+4 - 4=16 - 4$, so $3x=12$. Divide both sides by 3: $x = 4$.

Step4: Find the length of $\overline{LN}$

Substitute $x = 4$ into the expression for $LN$: $LN=12x + 16$. Then $LN=12\times4+16=48 + 16=64$.

Answer:

64 units