Answer
$x=\frac{1}{2}$.
Work Step by Step
The given equation is
$\Rightarrow 7+3x-12x=3x+1$
Simplify.
$\Rightarrow 7-9x=3x+1$
Add $9x-1$ to both sides.
$\Rightarrow 7-9x+9x-1=3x+1+9x-1$
Simplify.
$\Rightarrow 6=12x$
Divide both sides by $12$.
$\Rightarrow \frac{6}{12}=\frac{12x}{12}$
Simplify.
$\Rightarrow \frac{1}{2}=x$.
Check:-
$\Rightarrow 7+3(\frac{1}{2})-12(\frac{1}{2})=3(\frac{1}{2})+1$
$\Rightarrow 7+\frac{3}{2}-\frac{12}{2}=\frac{3}{2}+1$
$\Rightarrow \frac{14}{2}+\frac{3}{2}-\frac{12}{2}=\frac{3}{2}+\frac{2}{2}$
$\Rightarrow \frac{14+3-12}{2}=\frac{3+2}{2}$
$\Rightarrow \frac{5}{2}=\frac{5}{2}$
True.
Hence, the solution is $x=\frac{1}{2}$.
