We are given with an inequality and need to find it's solution set and need to represent it on number line too. Let's start !!!!
[tex]{:\implies \quad \sf 2(x+1)\> 3x-2}[/tex]
[tex]{:\implies \quad \sf 2x+2\> 3x-2}[/tex]
Subtracting 2x from both sides ;
[tex]{:\implies \quad \sf \cancel{2x}+2-\cancel{2x}\> 3x-2-2x}[/tex]
[tex]{:\implies \quad \sf 2\> x-2}[/tex]
Adding 2 to both sides :
[tex]{:\implies \quad \sf 2+2\> x-\cancel{2}+\cancel{2}}[/tex]
[tex]{:\implies \quad \sf 4\> x }[/tex]
[tex]{:\implies \quad \sf x\< 4}[/tex]
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{x\in (-\infty,4)}}}[/tex]
Refer to the attachment for representation
