$$( x - 2 ) ( x ^ { 2 } + 2 x + 4 ) \leq x ( x ^ { 2 } + 2 ) + 1$$
$x\geq -\frac{9}{2}$
$$x^{3}-8\leq x\left(x^{2}+2\right)+1$$
$$x^{3}-8\leq x^{3}+2x+1$$
$$x^{3}-8-x^{3}\leq 2x+1$$
$$-8\leq 2x+1$$
$$2x+1\geq -8$$
$$2x\geq -8-1$$
$$2x\geq -9$$
$$x\geq -\frac{9}{2}$$
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