First degree equation;:
A term that changes member changes sign
Fractions: Multiply the 2 members by the nominators least common multiple

Go !

$\LARGE 1 + x = 3$ $\LARGE x = 3-1\qquad : \qquad S=\{2\}$
$\LARGE 3+x=-x+3$ $\LARGE x+x = 3-3 \qquad;\qquad 2x = 0\qquad ;\qquad S =\{0\} $
$\LARGE 3+x=x+3$ $\LARGE x-x = 3-3 \qquad;\qquad 0x = 0\qquad ;\qquad S = \mathbb R $ ( All real numbers are solution !)
$\LARGE 3+2x=x+3$ $\LARGE 3x-x = 3-3 \qquad;\qquad 2x = 0\qquad ;\qquad S =\{0\}$
$\LARGE 3+x=2x+4$ $\LARGE x-2x = 4-3 \qquad;\qquad -x = 1\qquad;\qquad x = -1\qquad ;\qquad S =\{-1\} $