4 | x + 1 | − x 2 ≤ 2 ( x + 2 ) 4 | x + 1 | ≤ 2 ( x + 2 ) + x 2 − 2 ( x + 2 ) − x 2 ≤ 4 ( x + 1 ) ≤ x 2 + 2 ( x + 2 ) {\displaystyle {\begin{aligned}&4|x+1|-x^{2}\leq 2(x+2)\\&4|x+1|\leq 2(x+2)+x^{2}\\&-2(x+2)-x^{2}\leq 4(x+1)\leq x^{2}+2(x+2)\\\end{aligned}}}
4 x + 4 ≤ x 2 + 2 x + 4 x 2 − 2 x ≥ 0 x ( x − 2 ) ≥ 0 x ( x − 2 ) = 0 x 1 = 0 x 2 = 2 ↓ x ≤ 0 ; x ≤ 2 {\displaystyle {\begin{aligned}&4x+4\leq x^{2}+2x+4\\&x^{2}-2x\geq 0\\&x(x-2)\geq 0\\&x(x-2)=0\\&x_{1}=0&x_{2}=2\\&\downarrow \\&x\leq 0;x\leq 2\\\end{aligned}}}
x ≤ − 4 ; − 2 ≤ x ≤ 0 ; x ≥ 2 {\displaystyle {\begin{aligned}x\leq -4;-2\leq x\leq 0;x\geq 2\end{aligned}}}
