a)
\(512-\left(128-5x\right)=3x+12\\ 512-128+5x=3x+12\\ 384+5x=3x+12\\ 5x-3x=12-384\\ 2x=-372\\ x=\left(-372\right):2\\ x=-186\)
b)
\(\left(2x-1\right)+\left(4x-2\right)+...+\left(400x-200\right)=5+10+...+1000\\ \left(2x+4x+...+400x\right)-\left(1+2+...+200\right)=5+10+...+1000\\ x\left(2+4+...+400\right)=\left(5+10+...+1000\right)+\left(1+2+...+200\right)\\ 2x\cdot\left(1+2+...+200\right)=5\cdot\left(1+2+...+200\right)+1\cdot\left(1+2+...+200\right)\\ 2x\cdot\left(1+2+...+200\right)=\left(5+1\right)\cdot\left(1+2+...+200\right)\\ 2x\cdot\left(1+2+...+200\right)=6\cdot\left(1+2+...+200\right)\\ \Rightarrow2x=6\\ x=6:2\\ x=3\)
c)
\(\left(x+2\right)+\left(4x+4\right)+\left(7x+6\right)+...+\left(25x+18\right)+\left(28x+20\right)=1560\\ \left(x+4x+7x+...+25x+28x\right)+\left(2+4+6+...+18+20\right)=1560\\ x\left(1+4+7+...+25+28\right)+110=1560\\ 145x+110=1560\\ 145x=1560-110\\ 145x=1450\\ x=1450:145\\ x=10\)
d)
\(x+4x+5x+9x+14x+...+97x=500\\ x\left(1+4+5+9+14+...+97\right)=500\)
Dãy số trong ngoặc có quy luật: Số thứ \(n\) bằng số thứ \(n-1\) cộng số thứ \(n-2\)
Suy ra dãy số đó là: \(1+4+5+9+14+23+37+60+97=250\)
Thế vào ta được:
\(250x=500\\ x=500:250\\ x=2\)
e)
\(720-\left[41-\left(2x-5\right)\right]=2^3\cdot5\\ 720-41+\left(2x-5\right)=8\cdot5\\ 720-41+2x-5=40\\ \left(720-41-5\right)+2x=40\\ 674+2x=40\\ 2x=40-674\\ 2x=-634\\ x=\left(-634\right):2\\ x=-317\)
f)
\(697:\dfrac{15x+364}{x}=17\\ \dfrac{15x+364}{x}=697:17\\ \dfrac{15x+364}{x}=41\\ \dfrac{15x+364}{x}\cdot x=41x\\ 15x+364=41x\\ 364=41x-15x\\ 364=26x\\ x=364:26\\ x=14\)
