Answer
$x=\frac{1}{2}$.
Work Step by Step
The given equation is
$\Rightarrow 2(4x+2)= 4x-12(x-1)$
Use distributive property.
$\Rightarrow 8x+4= 4x-12x+12$
Simplify.
$\Rightarrow 8x+4= -8x+12$
Add $8x-4$ to both sides.
$\Rightarrow 8x+4+8x-4= -8x+12+8x-4$
Simplify.
$\Rightarrow 16x= 8$
Divide both sides by $16$.
$\Rightarrow \frac{16x}{16}=\frac{8}{16}$
Simplify.
$\Rightarrow x=\frac{1}{2}$
Check:-
$\Rightarrow 2(4(\frac{1}{2})+2)= 4(\frac{1}{2})-12((\frac{1}{2})-1)$
$\Rightarrow 2(2+2)= 2-12(\frac{1}{2}-1)$
$\Rightarrow 2(4)= 2-12(-\frac{1}{2})$
$\Rightarrow 8= 2+6$
$\Rightarrow 8= 8$
True.
Hence, the solution is $x=\frac{1}{2}$.
