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 \(LM = 10x + 8\), \(MN=5x - 4\), and \(LN = 12x + 16\) into the equation:
\((10x + 8)+(5x - 4)=12x + 16\)

Step2: Simplify the left - hand side

Combine like terms: \(10x+5x + 8 - 4=12x + 16\), so \(15x+4 = 12x + 16\)

Step3: Solve for \(x\)

Subtract \(12x\) from both sides: \(15x-12x+4=12x - 12x+16\), \(3x+4 = 16\)
Subtract \(4\) from both sides: \(3x+4 - 4=16 - 4\), \(3x=12\)
Divide both sides by \(3\): \(x=\frac{12}{3}=4\)

Step4: Find the length of \(LN\)

Substitute \(x = 4\) into \(LN=12x + 16\)
\(LN=12\times4+16\)
\(LN = 48+16\)
\(LN=64\)

Answer:

64 units