|3x−7|<2x+2−(2x+2)<3x−7<2x+2−2x−2<3x−75<5xx>13x−7<2x+2x<91<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}}}