Answers:
- Segments Bisector: M
- MQ = 7
======================================================
Step-by-step explanation:
Point M is the segment bisector because it splits PQ into the equal halves of PM and MQ. The tickmarks indicate this visually.
Since PM and MQ are the same length, we can set them equal to one another and solve for x.
5x-3 = 11 - 2x
5x+2x = 11+3
7x = 14
x = 14/7
x = 2
The 2 you have in the box seems to indicate this might be what you found for x. It's not the final answer because we need to determine MQ based on this. Let's find the length of each smaller piece.
- PM = 5x - 3 = 5*2 - 3 = 10 - 3 = 7
- MQ = 11 - 2x = 11 - 2*2 = 11 - 4 = 7
In short, MQ = 7
The fact that each piece is the same length (7 units) helps us verify we have the correct x value and correct final answer.