Question

if $lm = x + 1$, $mn = 2x$, and $ln = 7$, what is $mn$? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set up the equation

From the line segment, we know that \( LM + MN = LN \). Substituting the given expressions, we get \((x + 1) + 2x = 7\).

Step2: Solve for \( x \)

Combine like terms: \( x + 2x + 1 = 7 \) which simplifies to \( 3x + 1 = 7 \). Subtract 1 from both sides: \( 3x = 7 - 1 = 6 \). Then divide both sides by 3: \( x = \frac{6}{3} = 2 \).

Step3: Find \( MN \)

Since \( MN = 2x \), substitute \( x = 2 \) into the expression: \( MN = 2\times2 = 4 \).

Answer:

4