Question

previous answer: 5 lm = x + 12 ln = x + 15 find mn

Explanation:

Step1: Recall segment addition postulate

For collinear points \( L \), \( M \), \( N \) (where \( M \) is between \( L \) and \( N \)), we have \( LN = LM + MN \).

Step2: Substitute given expressions

We know \( LM = x + 12 \), \( LN = x + 15 \). Substitute into the formula: \( x + 15=(x + 12)+MN \).

Step3: Solve for \( MN \)

Subtract \( x + 12 \) from both sides: \( MN=(x + 15)-(x + 12) \). Simplify the right - hand side: \( MN=x + 15 - x - 12=3 \). Wait, but the previous answer is 5. Maybe there was a mis - reading of the diagram. Wait, maybe the diagram is \( L---M---N \), and \( LM=x + 12 \), \( LN=x + 15 \), so \( MN = LN - LM=(x + 15)-(x + 12)=3 \). But if the previous answer is 5, maybe the expressions are different. Wait, maybe the user made a typo, but following the segment addition:

If \( L \), \( M \), \( N \) are collinear with \( M \) between \( L \) and \( N \), then \( MN=LN - LM \).

Given \( LM=x + 12 \), \( LN=x + 15 \), then \( MN=(x + 15)-(x + 12)=3 \). But if the previous answer is 5, maybe the expressions are \( LM = x+2 \), \( LN=x + 7 \), but according to the given problem, with \( LM=x + 12 \) and \( LN=x + 15 \), \( MN = 3 \).

Wait, maybe the diagram is different. Let's re - examine. The points are \( L \), \( M \), \( N \) in order. So \( LN=LM + MN \). So \( MN=LN - LM=(x + 15)-(x + 12)=3 \).

Answer:

\( 3 \) (If we follow the given expressions. If the previous answer is 5, there might be an error in the given expressions or the diagram interpretation.)