$M_1 = \text{Moment at prop support}$
$M_1 = -\frac{1}{2}(4)(200)[ \, \frac{2}{3}(4) \, ] - \frac{1}{2}(4)(120)[ \, \frac{1}{3}(4) \, ]$
$M_1 = -1386.67 ~ \text{lb}\cdot\text{ft}$
$M_1L_1 + 2M_2(L_1 + L_2) + M_3L_2 + \dfrac{6A_1\bar{a}_1}{L_1} + \dfrac{6A_2\bar{b}_2}{L_2} = 0$
$-1386.67(6) + 2M_{wall}(6 + 0) + 0 + \frac{7}{60}(120)(6^3) + 0 = 0$
$-8320.02 + 12M_{wall} + 3024 = 0$
$12M_{wall} = 5296.02$
$M_{wall} = 441.335 ~ \text{lb}\cdot\text{ft}$ answer
$M_{wall} = \Sigma M_{\text{to the left of wall}}$
$441.33 = 6R - \frac{1}{2}(10)(200)[ \, \frac{2}{3}(10) \, ]$
$R = 1184.67 ~ \text{lb}$ answer
Check by Moment-Diagram by Parts
$A_1 = \frac{1}{2}(6)(6R) = 18R$
$x_1 = \frac{1}{3}(6) = 2 ~ \text{ft}$
$A_2 = \frac{1}{4}(10)(\frac{10\,000}{3}) - \frac{1}{4}(4)(\frac{640}{3}) = 8\,120 ~ \text{lb}\cdot\text{ft}^3$
$x_2 = \dfrac{\frac{1}{4}(10)(\frac{10\,000}{3})(\frac{10}{5}) - \frac{1}{4}(4)(\frac{640}{3})(6 + \frac{4}{5})}{8\,120} = 1.8739 ~ \text{ft}$
$A_3 = \frac{1}{3}(10)(10\,000) - \frac{1}{3}(4)(1600) = 31\,200 ~ \text{lb}\cdot\text{ft}^3$
$x_3 = \dfrac{\frac{1}{3}(10)(10\,000)(\frac{10}{4}) - \frac{1}{3}(4)(1600)(6 + \frac{4}{4})}{31\,200} = 2.1923 ~ \text{ft}$
$EI \, t_{B/A} = 0$
$(\text{Area}_{AB}) \cdot \bar{X}_B = 0$
$A_1(6 - x_1) + A_2(6 - x_2) - A_3(6 - x_3) = 0$
$18R(6 - 2) + 8\,120(6 - 1.8739) - 31\,200(6 - 2.1923) = 0$
$R = 1184.67 ~ \text{lb}$ okay
