Упр.985 ГДЗ Макарычев Миндюк 8 класс (Алгебра)

1. а)

   $$\begin{aligned} 2(x-1)-3(x-2)<x,\\ 6x-3≤17-(x-5) \end{aligned}$$
   $$\begin{aligned} 2x-2-3x+6≤x,\\ 6x-3≤17-x+5 \end{aligned}$$
   $$\begin{aligned} -x+4≤x,\\ 7x≤25 \end{aligned}$$
   $$\begin{aligned} 2x≥4,\\ x≤\frac{25}{7} \end{aligned}$$
   $$x>2,\quad x<\frac{25}{7}$$
   $$x\in\left(2;\frac{25}{7}\right).$$

2. б)

   $$\begin{aligned} 3{,}3-3(1{,}2-5x)>0{,}6(10x+1),\\ 1{,}6-4{,}5(4x-1)<2x+26{,}1 \end{aligned}$$
   $$\begin{aligned} 3{,}3-3{,}6+15x&>6x+0{,}6,\\ 1{,}6-18x+4{,}5&<2x+26{,}1 \end{aligned}$$ $$\begin{aligned} 9x&>0{,}9,\\ -20x&<20 \end{aligned}$$ $$\begin{aligned} x&>0{,}1,\\ x&>-1 \end{aligned}$$
   $$x\in(0{,}1;+\infty).$$

3. в)

   $$\begin{aligned} 5{,}8(1-a)-1{,}8(6-a)<5,\\ 8-4(2-5a)>-(5a+6) \end{aligned}$$
   $$\begin{aligned} 5{,}8-5{,}8a-10{,}8+1{,}8a&<5,\\ 8-8+20a&>-5a-6 \end{aligned}$$
   $$\begin{aligned} -4a&<10,\\ 25a&>-6 \end{aligned}$$
   $$\begin{aligned} a&>-2{,}5,\\ a&>-0{,}24 \end{aligned}$$
   $$a\in(-0{,}24;+\infty).$$

4. г)

   $$\begin{aligned} x(x-1)-(x^2-10)<1-6x,\\ 3{,}5-(x-1{,}5)<6-4x \end{aligned}$$
   $$\begin{aligned} x^2-x-x^2+10&<1-6x,\\ 3{,}5-x+1{,}5&<6-4x \end{aligned}$$ $$\begin{aligned} -x+10&<1-6x,\\ 5-x&<6-4x \end{aligned}$$ $$\begin{aligned} 5x&<-9,\\ 3x&<1 \end{aligned}$$ $$\begin{aligned} x&<-\frac{9}{5},\\ x&<\frac{1}{3} \end{aligned}$$ $$x\in\left(-\infty;-\frac{9}{5}\right).$$

5. а)

   $$3^{-4}\cdot 3^6=3^{2}=9$$

6. б)

   $$2^4\cdot 2^{-3}=2^{1}=2$$

7. в)

   $$10^8\cdot 10^{-5}\cdot 10^{-6}=10^{-3}=0{,}001$$

8. г)

   $$2^{10}:2^{12}=2^{-2}=\frac{1}{4}=0{,}25$$

9. д)

   $$5^{-3}:5^{-3}=5^0=1$$

10. е)

    $$3^{-4}:3=3^{-5}=\frac{1}{243}$$

11. ж)

    $$(2^{-4})^{-1}=2^4=16$$

12. з)

    $$(5^2)^{-2}\cdot 5^3=5^{-4}\cdot 5^3=5^{-1}=\frac{1}{5}=0{,}2$$

13. и)

    $$3^{-4}\cdot(3^{-2})^{-4}=3^{-4}\cdot 3^8=3^4=81$$

Ответ

а) $$x\in\left(2;\frac{25}{7}\right)$$; б) $$x\in(0{,}1;+\infty)$$; в) $$a\in(-0{,}24;+\infty)$$; г) $$x\in\left(-\infty;-\frac{9}{5}\right)$$; а) $$9$$; б) $$2$$; в) $$0{,}001$$; г) $$0{,}25$$; д) $$1$$; е) $$\frac{1}{243}$$; ж) $$16$$; з) $$0{,}2$$; и) $$81$$.