| 2 − 4 x | − 4 ≥ 0 | 2 − 4 x | ≥ 4 2 − 4 x ≥ 4 ; 2 − 4 x ≥ − 4 2 − 4 x ≥ 4 − 4 x ≥ 2 x ≤ − 1 2 2 − 4 ≤ − 4 − 4 x ≤ − 6 x ≥ − 1 1 2 x ≤ − 1 2 ; x ≥ − 1 1 2 {\displaystyle {\begin{aligned}&|2-4x|-4\geq 0\\&|2-4x|\geq 4\\&2-4x\geq 4;2-4x\geq -4\\&\color {blue}2-4x\geq 4\\&\color {blue}-4x\geq 2\\&\color {blue}x\leq {\frac {-1}{2}}\\&\color {red}2-4\leq -4\\&\color {red}-4x\leq -6\\&\color {red}x\geq -1{\frac {1}{2}}\\&\color {Violet}x\leq {\frac {-1}{2}};x\geq -1{\frac {1}{2}}\\\end{aligned}}}
