Упр.295 ГДЗ Муравин 7 класс (Алгебра)

1) 2/9 (0,9 — 1 2/7 x) + x = 10; 3) (2x-3)/4 — 1 = x + (x+5)/3;
2) 8 (5 — 1 1/4 b) = 3b + 14; 4) (3x+1)/2 + 2 = (x+1)/7 — x.

1. $$\frac{2}{9}\left(0{,}9-1\frac{2}{7}x\right)+x=10$$

   $$0{,}9=\frac{9}{10}, \quad 1\frac{2}{7}=\frac{9}{7}$$

   $$\frac{2}{9}\left(\frac{9}{10}-\frac{9}{7}x\right)+x=10$$

   $$\frac{1}{5}-\frac{2}{7}x+x=10$$

   $$\frac{5}{7}x=10-\frac{1}{5}=\frac{49}{5}$$

   $$x=\frac{49}{5}:\frac{5}{7}=\frac{49}{5}\cdot\frac{7}{5}=\frac{343}{25}=13\frac{18}{25}$$

2. $$8\left(5-1\frac{1}{4}b\right)=3b+14$$

   $$1\frac{1}{4}=\frac{5}{4}$$

   $$8\left(5-\frac{5}{4}b\right)=3b+14$$

   $$40-10b=3b+14$$

   $$-13b=14-40=-26$$

   $$b=2$$

3. $$\frac{2x-3}{4}-1=x+\frac{x+5}{3}$$

   $$\frac{2x-3-4}{4}=\frac{3x+x+5}{3}$$

   $$\frac{2x-7}{4}=\frac{4x+5}{3}$$

   $$3(2x-7)=4(4x+5)$$

   $$6x-21=16x+20$$

   $$-10x=41$$

   $$x=-\frac{41}{10}=-4{,}1$$

4. $$\frac{3x+1}{2}+2=\frac{x+1}{7}-x$$

   $$\frac{3x+1+4}{2}=\frac{x+1-7x}{7}$$

   $$\frac{3x+5}{2}=\frac{1-6x}{7}$$

   $$7(3x+5)=2(1-6x)$$

   $$21x+35=2-12x$$

   $$33x=-33$$

   $$x=-1$$

Ответ

$$1)\ x=13\frac{18}{25};\quad 2)\ b=2;\quad 3)\ x=-4{,}1;\quad 4)\ x=-1.$$