5. Решите уравнение: 1. -3d-10 = 3d-6 2. -1,6-0,3p = 0,9p + 0,2 3. 4(x-6) = x-9 4. (8x+3) - (10x+6) = 9 5. 0,3(6-3y) - 4,5 - 0,8(y-9) 6. \(\frac{x+7}{3} - \frac{2x+3}{5}\) 7. \(\frac{5x+4}{2} + 3 = \frac{9y}{4}\) 8. \(\frac{x+8}{2} + \frac{3-2x}{5} = 3;\)

Решение:

1. \(-3d-10 = 3d-6 \Rightarrow -10+6 = 3d+3d \Rightarrow -4 = 6d \Rightarrow d = -\frac{4}{6} = -\frac{2}{3}\)
2. \(-1,6-0,3p = 0,9p + 0,2 \Rightarrow -1,6-0,2 = 0,9p+0,3p \Rightarrow -1,8 = 1,2p \Rightarrow p = -\frac{1,8}{1,2} = -\frac{18}{12} = -\frac{3}{2}\)
3. \(4(x-6) = x-9 \Rightarrow 4x-24 = x-9 \Rightarrow 4x-x = -9+24 \Rightarrow 3x = 15 \Rightarrow x = 5\)
4. \((8x+3) - (10x+6) = 9 \Rightarrow 8x+3-10x-6 = 9 \Rightarrow -2x-3 = 9 \Rightarrow -2x = 12 \Rightarrow x = -6\)
5. \(0,3(6-3y) - 4,5 - 0,8(y-9) = 1,8-0,9y-4,5-0,8y+7,2 = -1,7y + 4,5 = 0 \Rightarrow -1,7y = -4,5 \Rightarrow y = \frac{4,5}{1,7} = \frac{45}{17}\)
6. \(\frac{x+7}{3} - \frac{2x+3}{5} = 0 \Rightarrow 5(x+7) - 3(2x+3) = 0 \Rightarrow 5x+35 - 6x-9 = 0 \Rightarrow -x+26 = 0 \Rightarrow x = 26\)
7. \(\frac{5x+4}{2} + 3 = \frac{9y}{4} \Rightarrow 2(5x+4) + 12 = 9y \Rightarrow 10x+8+12 = 9y \Rightarrow 10x+20 = 9y\)
8. \(\frac{x+8}{2} + \frac{3-2x}{5} = 3 \Rightarrow 5(x+8) + 2(3-2x) = 30 \Rightarrow 5x+40+6-4x = 30 \Rightarrow x+46 = 30 \Rightarrow x = -16\)

Ответ: 1) \(d = -\frac{2}{3}\); 2) \(p = -\frac{3}{2}\); 3) \(x = 5\); 4) \(x = -6\); 5) \(y = \frac{45}{17}\); 6) \(x = 26\); 7) \(10x+20 = 9y\); 8) \(x = -16\).