Answer
[-1, 1] U {7/2}
Work Step by Step
$(2x-7)^4(x-1)^3(x+1) \leq 0$
Find the roots of the function
$x = -1, 1, 7/2$
Test numbers in between those zero values to determine if the function is negative or positive
(-∞, -1] $(+)(-)(-) = (+)$
[-1, 1] $(+)(-)(+) = (-)$
[1, 7/2] $(+)(+)(+) = (+)$
[7/2, ∞) $(+)(+)(+) = (+)$
Thus the solution is [-1, 1] U {7/2} (as 7/2 is a root that has the function equal to 0, thus satisfying the inequality)
