| 3 x + 9 | < 15 − x − ( 15 − x ) < 3 x + 9 < 15 − x − 15 + x < 3 x + 9 2 x > − 24 x > − 12 3 x + 9 < 15 − x 4 x < 6 x < 1 1 2 − 12 < x < 1 1 2 {\displaystyle {\begin{aligned}&|3x+9|<15-x\\&-(15-x)<3x+9<15-x\\&\color {blue}-15+x<3x+9\\&\color {blue}2x>-24\\&\color {blue}x>-12\\&\color {red}3x+9<15-x\\&\color {red}4x<6\\&\color {red}x<1{\frac {1}{2}}\\&\color {Violet}-12<x<1{\frac {1}{2}}\\\end{aligned}}}
