Question

3/4 + a = 5/6 - 1/2x

Answer 1

It is not clear whether it is  (1/2) * x  or  1/(2x).   I do it both ways.  You should use parentheses for clearly writing question.

$\frac{3}{4}+a=\frac{5}{6}-\frac{1}{2}x\\ \\-\frac{x}{2}=a+\frac{3}{4}-\frac{5}{6}=a+\frac{9-10}{12}=a-\frac{1}{12}\\ \\x=-2(a-\frac{1}{12})\\ \\x=-2a+\frac{1}{6}$

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$\frac{3}{4}+a=\frac{5}{6}-\frac{1}{2x}\\ \\-\frac{1}{2x}=a+\frac{3}{4}-\frac{5}{6}\\ \\=a+\frac{9-10}{12}\\ \\-\frac{1}{2x}=a-\frac{1}{12}\\ \\\frac{1}{x}=-2a+\frac{2}{12}=\frac{-12a+1}{6}\\ \\x = \frac{6}{1-12a}$

Answer 2

0.75a=-0.0833333333333333x is the answer of 3/4+a=5/6-1/2x by calculate method......