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Solving Equations for One Variable

Solve: $\ 6a+6=7a-5a+3$

$6a+6=2a+3$

$6a+6-2a=2a+3-2a$

$4a+6=3$

$4a+6-6=3-6$

$4a=-3$

$a=-\frac{3}{4}$

Check:

LHS: $6(-\frac{3}{4})+6=-\frac{9}{2}+6=-\frac{9}{2}+\frac{12}{2}=\frac{3}{2}=1\frac{1}{2}$

RHS: $2(-\frac{3}{4})+3=-\frac{3}{2}+3=-\frac{3}{2}+\frac{6}{2}=\frac{3}{2}=1\frac{1}{2}$