Answer
$(-\infty,2)$.
The number line is shown below.
Work Step by Step
The given expression is
$\Rightarrow 2(x+3)>6-\{4[x-(3x-4)-x]+4\}$
Apply the distributive property and clear the parentheses.
$\Rightarrow 2x+6>6-\{4[x-3x+4-x]+4\}$
Add like terms.
$\Rightarrow 2x+6>6-\{4[-3x+4]+4\}$
Apply the distributive property and clear the square bracket.
$\Rightarrow 2x+6>6-\{-12x+16+4\}$
Add like terms.
$\Rightarrow 2x+6>6-\{-12x+20\}$
Apply distributive property and clear the curly bracket.
$\Rightarrow 2x+6>6+12x-20$
Add like terms.
$\Rightarrow 2x+6>12x-14$
Add $-2x+14$ to both sides.
$\Rightarrow 2x+6-2x+14>12x-14-2x+14$
Simplify.
$\Rightarrow 20>10x$
Divide both sides by $10$.
$\Rightarrow \frac{20}{10}>\frac{10x}{10}$
Simplify.
$\Rightarrow 2>x$
The solution set is $(-\infty,2)$.
