pertidaksamaan 2^2x+1-5.2^2x+1+8>0

2²ˣ⁺¹ - 5.2²ˣ⁺¹+ 8 > 0
2.2²ˣ - 2.5.2²ˣ + 8 > 0
Misal : 2ˣ = a, maka :
2a² - 10a² + 8 > 0
-8a² + 8 > 0
8 ( -a² + 1) > 0
-a² + 1 > 0
1 > a²
a < 1
///ralat/
2ˣ < 1
2ˣ < 2⁰
x < 0
Jadi, HP = { x | x < 0 , x ∈ R }
Semoga bisa membantu, Maaf, tadi jawabannya salah.

2^(2x + 1) - 5 . 2^(2x + 1) + 8 > 0
Misal 2^(2x + 1) = p
p - 5p + 8 > 0
-4p > -8
4p < 8
p < 2
2^(2x + 1) < 2^1
2x + 1 < 1
2x < 0
x < 0