a) [tex]3\left(x-5\right)+x=2-x\\4x-15=2-x\\4x-15+15=2-x+15\\4x=-x+17\\5=17\\\frac{5x}{5}=\frac{17}{5}\\x=\frac{17}{5}\\x=\boxed{3\frac{2}{5}}[/tex]
b) [tex]x+\frac{2}{3}+x=3-2x\\x+x+\frac{2}{3}=3-2x\\2x+\frac{2}{3}=3-2x\\2x+\frac{2}{3}-\frac{2}{3}=3-2x-\frac{2}{3}\\2x=-2x+\frac{7}{3}\\2x+2x=-2x+\frac{7}{3}+2x\\4x=\frac{7}{3}\\\frac{4x}{4}=\frac{\frac{7}{3}}{4}\\x=\boxed{\frac{7}{12}}[/tex]
c) [tex]a-2x-\frac{5}{2}=3-1\\a-2x-\frac{5}{2}=2\\a-2x-\frac{5}{2}-a=2-a\\-2x-\frac{5}{2}=2-a\\-2x-\frac{5}{2}+\frac{5}{2}=2-a+\frac{5}{2}\\-2x=-a+\frac{9}{2}\\\frac{-2x}{-2}=-\frac{a}{-2}+\frac{\frac{9}{2}}{-2}\\x=\boxed{-\frac{-2a+9}{4}}[/tex]