Question

bisector: yes or no? 6. m is between l and n. lm = 7x - 1, mn = 2x + 4, and ln = 12. find the value of x an determine if m is a bisector. x = __________ bisector: yes or no?

Explanation:

Step1: Use segment addition postulate

Since M is between L and N, we know that \( LM + MN = LN \). Substituting the given expressions, we get \((7x - 1)+(2x + 4)=12\).

Step2: Simplify the equation

Combine like terms: \( 7x+2x - 1 + 4 = 12 \), which simplifies to \( 9x + 3 = 12 \).

Step3: Solve for x

Subtract 3 from both sides: \( 9x = 12 - 3 = 9 \). Then divide both sides by 9: \( x=\frac{9}{9}=1 \).

Step4: Find LM and MN

Substitute \( x = 1 \) into \( LM = 7x - 1 \): \( LM = 7(1)-1 = 6 \). Substitute \( x = 1 \) into \( MN = 2x + 4 \): \( MN = 2(1)+4 = 6 \).

Step5: Determine if M is a bisector

A bisector of a segment divides it into two equal parts. Since \( LM = MN = 6 \) and \( LN = 12 \), M bisects LN.

Answer:

\( x = 1 \)
Bisector: YES