Question

problem 18: (first taught in lesson 8) if l - m - n, and if lm = 2x, mn = 3x - 1, and ln = 24, then find mn. after you enter your answer press go. mn =

Explanation:

Step1: Apply segment - addition postulate

Since \(L - M - N\), we know that \(LM+MN = LN\). Substitute the given expressions: \(2x+(3x - 1)=24\).

Step2: Simplify the left - hand side

Combine like terms: \(2x+3x-1 = 5x-1\). So, \(5x - 1=24\).

Step3: Solve for \(x\)

Add 1 to both sides of the equation: \(5x-1 + 1=24 + 1\), which gives \(5x=25\). Then divide both sides by 5: \(x=\frac{25}{5}=5\).

Step4: Find \(MN\)

Substitute \(x = 5\) into the expression for \(MN\). Since \(MN=3x - 1\), then \(MN=3\times5-1=15 - 1 = 14\).

Answer:

14