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 \(M\) lies between \(L\) and \(N\), \(LM + MN=LN\).
Substitute the given expressions: \((10x + 8)+(5x - 4)=12x + 16\).

Step2: Simplify the left - hand side

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 \(3x+4 = 16\).
Subtract \(4\) from both sides: \(3x+4 - 4=16 - 4\), so \(3x=12\).
Divide both sides by \(3\): \(x=\frac{12}{3}=4\).

Step4: Find the length of \(LN\)

Substitute \(x = 4\) into \(LN=12x + 16\).
\(LN=12\times4+16\).
First, calculate \(12\times4 = 48\), then \(48+16=64\).

Answer:

64 units