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 64 units 40 units 48 units

Explanation:

Step1: Set up equation

Since $LN = LM+MN$, we have $12x + 16=(10x + 8)+(5x - 4)$.

Step2: Simplify equation

$12x+16 = 10x+8 + 5x-4$, which simplifies to $12x+16=15x + 4$.

Step3: Solve for x

Subtract $12x$ from both sides: $16 = 3x+4$. Then subtract 4 from both sides: $12 = 3x$. So $x = 4$.

Step4: Find length of LN

Substitute $x = 4$ into $LN=12x + 16$. $LN=12\times4+16=48 + 16=64$.

Answer:

64 units