Question

Решите неравенство: 1). 2). 3). 4). 5). 6). 7).

Answer 1

$1. \ (\frac{5}{3})^{5x+2}$
$2. \ 7^{x^{2} -x+3} \leq (\frac{1}{7})^{5x}, \\ 7^{x^{2} -x+3} \leq 7^{-5x}, \\ x^{2} -x+3 \leq -5x, \\ x^{2} +4x+3 \leq0, \\ x^{2} +4x+3=0, \\ x_1=-3, x_2=-1, \\ (x+3)(x+1) \leq 0, \\ -3 \leq x \leq -1; \\$
$3. \ 4\cdot4^{-x}-9\cdot 2^{-x}+20, \\ 2^{-x}=a, 4a^2-9a+20, \\ 4a^2-9a+2=0, \\ D=49, \\ a_1= \frac{1}{4} , a_2=2, \\ \left [ {{a< \frac{1}{4},} \atop {a2;}} \right. \left [ {{2^{-x}2;}} \right. \left [ {{-x1;}} \right. \left [ {{x2,} \atop {x$
$4. \ \sqrt{2^{-x}} \leq 128, \\ 2^{-\frac{x}{2} } \leq 2^7, \\ -\frac{x}{2} \leq 7, \\ x \geq -14; \\$
$5. \ 1,25^{8x-5} 0,8^{3x+2}, \\ 0,8^{5-8x} 0,8^{3x+2}, \\ 5-8x3, \\ x \frac{3}{11}; \\$
$6. \ 5^{ \frac{ x^{2} -3x-2}{6-x} } \geq 0,2, \\ 0,2^{ \frac{ x^{2} -3x-2}{x-6} } \geq 0,2, \\ \frac{x^{2} -3x-2}{x-6} \leq 1, \\ \frac{x^{2} -4x+4}{x-6} \leq 0, \\ x-6 \neq 0, x \neq 6, \\ (x-2)^2(x-6) \leq 0, \\ \left [ {{x=2,} \atop {x$
$7. \ 3\cdot( \frac{1}{9})^{x}-28\cdot(\frac{1}{3})^{x}+9$