Answer
$[-1/3, 1/2] U [1, ∞ )$
Work Step by Step
$x^2 (7-6x) \leq 1$
Find the roots of the function
$7x^2 - 6x^3 - 1 \leq 0$
From the graph attached below with the zeros highlighted, the zeros are at:
$x = -1/3, 1/2, 1$
Thus the factored equation is $(-3x - 1)(2x-1)(x-1)$
Test numbers in between those zero values to determine if the function is negative or positive
(-∞, -1/3] $(+)(-)(-) = (+)$
[-1/3, 1/2] $(-)(-)(-) = (-)$
[1/2, 1] $(-)(+)(-) = (+)$
[1, ∞) $(-)(+)(+) = (-)$
Thus the solution is $[-1/3, 1/2] U [1, ∞ )$
