Объяснение:
(2ˣ⁻¹-1)/(2ˣ⁺¹+1)<1/2
((2ˣ⁻¹-1)/(2ˣ⁺¹+1))-(1/2)<0
(2*(2ˣ⁻¹-1)-1*(2ˣ⁺¹+1)/(2*(2ˣ⁺¹+1))<0
(2ˣ-2-2ˣ⁺¹-2)/(2*(2ˣ⁺¹+1))<0
(2ˣ-2*2ˣ-4)/(2*(2ˣ⁺¹+1))<0
(-2ˣ-4)/(2*(2ˣ⁺¹+1))<0
-(2ˣ+4)/(2*(2ˣ⁺¹+1))<0 |×(-2)
(2ˣ+4)/(2ˣ⁺¹+2)>0
2ˣ+4>0
2ˣ⁺¹+2>0 ⇒
(2ˣ+4)/(2ˣ⁺¹+2)≡>0
ответ: x∈(-∞;+∞).
Объяснение:
(2ˣ⁻¹-1)/(2ˣ⁺¹+1)<1/2
((2ˣ⁻¹-1)/(2ˣ⁺¹+1))-(1/2)<0
(2*(2ˣ⁻¹-1)-1*(2ˣ⁺¹+1)/(2*(2ˣ⁺¹+1))<0
(2ˣ-2-2ˣ⁺¹-2)/(2*(2ˣ⁺¹+1))<0
(2ˣ-2*2ˣ-4)/(2*(2ˣ⁺¹+1))<0
(-2ˣ-4)/(2*(2ˣ⁺¹+1))<0
-(2ˣ+4)/(2*(2ˣ⁺¹+1))<0 |×(-2)
(2ˣ+4)/(2ˣ⁺¹+2)>0
2ˣ+4>0
2ˣ⁺¹+2>0 ⇒
(2ˣ+4)/(2ˣ⁺¹+2)≡>0
ответ: x∈(-∞;+∞).