To simplify this inequality, we first expand the cubed terms on the left side:
(x-1)³ = x³ - 3x² + 3x - 1(x+1)³ = x³ + 3x² + 3x + 1
Therefore, the left side of the inequality becomes:
(x³ - 3x² + 3x - 1) - (x³ + 3x² + 3x + 1)= x³ - 3x² + 3x - 1 - x³ - 3x² - 3x - 1= -6x²
Now, the inequality becomes:
-6x² ≤ x - 6x²
By adding 6x² to both sides:
0 ≤ x
Therefore, the solution to the inequality is x ≥ 0.
To simplify this inequality, we first expand the cubed terms on the left side:
(x-1)³ = x³ - 3x² + 3x - 1
(x+1)³ = x³ + 3x² + 3x + 1
Therefore, the left side of the inequality becomes:
(x³ - 3x² + 3x - 1) - (x³ + 3x² + 3x + 1)
= x³ - 3x² + 3x - 1 - x³ - 3x² - 3x - 1
= -6x²
Now, the inequality becomes:
-6x² ≤ x - 6x²
By adding 6x² to both sides:
0 ≤ x
Therefore, the solution to the inequality is x ≥ 0.