Question

1. 6x - 11 10x - 51 p m q

Explanation:

Assuming \( M \) is the midpoint of segment \( PQ \), so \( PM = MQ \).

Step 1: Set up the equation

Since \( PM = MQ \), we have \( 6x - 11 = 10x - 51 \).

Step 2: Solve for \( x \)

Subtract \( 6x \) from both sides:
\( -11 = 4x - 51 \)

Add 51 to both sides:
\( 40 = 4x \)

Divide both sides by 4:
\( x = 10 \)

If we want to find the length of \( PM \) or \( MQ \), substitute \( x = 10 \) into \( 6x - 11 \):
\( 6(10) - 11 = 60 - 11 = 49 \)
Or into \( 10x - 51 \):
\( 10(10) - 51 = 100 - 51 = 49 \)

(If the problem was to find \( x \), the answer is \( x = 10 \); if to find the length, it's 49. Since the problem wasn't fully specified, but the common case with midpoints is solving for \( x \) or the length. Assuming solving for \( x \) here.)

Answer:

\( x = 10 \) (or length \( 49 \) if finding segment length)