Solving McCauley's Beam Problem: Expert Tips for Success

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ShaunG123
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Poster has been reminded to show their work on schoolwork problems
Homework Statement
Using McCauley's to solve a beam problem
Relevant Equations
Beam Calculations
Can you help me answer this question please?
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Here is the question along with my solution below however I have been told this is wrong and an equation for the defelction and displacement is needed and answers for this along with a bending moment to support.
upload beam.png

beam calc 1.png
beam calc 2 (2).png
beam calc 3 (2).png
 
It seems there are some errors in resolving Mx-x:
The length 5 of the distributed load is not shown (although included in calculation).
The products of 111.75x and -50x are missing.
The correct equation may be:
##M_{x-x}=1032.5-215x##
 
I am really struggling to understand this to be honest is ymax my total deflection if so what would be max displacement
 
This is my attempt however I need to know a value/equation for displacement and deflection.
beam calc 1.png
beam calc 2 (2).png
beam calc 3 (2).png