| 3 x − 7 | < 2 x + 2 − ( 2 x + 2 ) < 3 x − 7 < 2 x + 2 − 2 x − 2 < 3 x − 7 5 < 5 x x > 1 3 x − 7 < 2 x + 2 x < 9 1 < x < 9 {\displaystyle {\begin{aligned}&|3x-7|<2x+2\\&-(2x+2)<3x-7<2x+2\\&\color {blue}-2x-2<3x-7\\&\color {blue}5<5x\\&\color {blue}x>1\\&\color {red}3x-7<2x+2\\&\color {red}x<9\\&\color {Purple}1<x<9\\\end{aligned}}}
