point m lies between points l and n on $overline{ln}$. if $ln = 12x + 16$, what is the length of…

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

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

Answer

Explanation:

Step1: Set up the equation

Since point M lies between L and N, $LN = LM+MN$. So, $12x + 16=(10x + 8)+(5x - 4)$.

Step2: Simplify the right - hand side

$(10x + 8)+(5x - 4)=10x+5x + 8 - 4=15x + 4$. So the equation becomes $12x + 16=15x + 4$.

Step3: Solve for x

Subtract $12x$ from both sides: $16 = 3x+4$. Then subtract 4 from both sides: $3x=12$. Divide both sides by 3, we get $x = 4$.

Step4: Find the length of LN

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

Answer:

64 units