nilai x yang memenuhi pertidaksamaan

Diketahui,
(1/8)^2x-x^2 ≤ 2^x^2-3x+5
(=) (1/2^3)^2x-x^2 ≤ 2^x^2-3x+5
(=) (2^-3)^2x-x^2 ≤ 2^x^2-3x+5
(=) 2^-3(2x-x^2) ≤ 2^x^2-3x+5
(=) -3(2x - x^2) ≤ x^2 - 3x + 5
(=) -6x + 3x^2 ≤ x^2 - 3x + 5
(=) 3x^2 - x^2 - 6x + 3x - 5 ≤ 0
(=) 2x^2 - 3x - 5 ≤ 0
(=) (2x - 5)(x + 1) ≤ 0

(=) 2x - 5 = 0
(=) 2x = 5
(=) x = 5/2
(=) x = 2,5

atau
(=) x + 1 = 0
(=) x = -1

Hp = {x|x ≤ -1 atau x ≤ 2,5}

(1/8)^(2x - x^2) ≤ 2^(x^2 - 3x + 5)
2^-3(2x - x^2) ≤ 2^(x^2 - 3x + 5)
-3(2x - x^2) ≤ x^2 - 3x + 5
-6x + 3x^2 - x^2 + 3x - 5 ≤ 0
2x^2 - 3x - 5 ≤ 0
(2x - 5)(x + 1) ≤ 0
x = 5/2 atau x = -1
Garis bilangan
+++ (-1) --- (5/2) +++
-1 ≤ x ≤ 5/2
-1 ≤ x ≤ 2 1/2