7) 0,25^(2.5-0.5x²)> 1/16
(1/4)^(2.5-0.5x²)> (1/4)²
2.5-0.5x²<2<br>-0.5x²+2.5-2<0<br>-0.5x²+0.5<0<br>x² -1>0
(x-1)(x+1)>0
x=1 x= -1
+ - +
------- -1 ---------- 1 ------------
\\\\\\\\\\ \\\\\\\\\\\\\\\\
x∈(-∞; -1)U(1; +∞)
8) (1/3)^(x)>9^(2x-1)
3^(-x)>3^(2(2x-1))
-x>4x-2
-x-4x>-2
-5x>-2
x<0.4<br>x∈(-∞; 0,4)
9) 4^(1-x)≤(1/2)^(3x+2)
2^(2(1-x))≤2^(-(3x+2))
2-2x≤ -3x-2
-2x+3x≤ -2-2
x≤ -4
x∈(-∞; -4]
10) (1/7)^(-9x²-8x+3)<7^(-7x²)<br>7^(-(-9x²-8x+3))<7^(-7x²)<br>9x²+8x-3<-7x²<br>9x²+7x²+8x-3<0<br>16x²+8x-3<0<br>16x²+8x-3=0
D=64-4*16*(-3)=64+192=256
x₁= -8-16 = -24/32 = -0.75
32
x₂= -8+16 = 8/32=1/4=0.25
32
+ - +
----------- -0.75 --------- 0.25 -----------
\\\\\\\\\\\\\
x∈(-0.75; 0,25)
11) 5^(2/x)≤0.2^(x-3)
5^(2/x)≤5^(-(x-3))
2/x≤ -x+3
ОДЗ: х≠0
2 + x - 3≤0
x
2+x² -3x ≤ 0
x
x² -3x+2 ≤0
x
Разложим x²-3x+2 на множители:
x²-3x+2=0
D=9-8=1
x₁=3-1 = 1
2
x₂= 3+1 = 2
2
x²-3x+2=(x-1)(x-2)
(x-1)(x-2) ≤0
x
x(x-1)(x-2)≤0
x=0 x=1 x=2
- + - +
------- 0 ------- 1------------ 2 ----------
\\\\\\\\ \\\\\\\\\\\\\\\\
x∈(-∞; 0)U[1; 2]