Question

решите неравенства №32.30 помогите мне пожалуйста

Answer 1

1) $(3x-1)^{2} -7<(9x+2)x+2\\9x^2-6x+1-7<9x^2+2x+2\\  9x^2-6x-9x^2-2x<2-1+7\\ -8x<8\\x<-1$

2) $2x(8x+3)+1>(5-4x)^2-1\\ 16x^2+6x+1>25-40x+16x^2-1\\ 16x^2+6x+40x-16x^2>25-1-1\\ 46x>23\\ x>\frac{23}{46}$

3)$(0.3x+0.2)^2+0.58x>3.9-(2-0.3x)(2+0.3x)\\ 0.09x^2+0.12x+0.04+0.58x>3.9-(4-0.09x^2)\\ 0.09x^2+0.7x+0.04-3.9+4-0.09x^2>0\\ 0.7x+0.14>0\\ 0.7x>-0.14\\ x>-0.2$

4) $(0.2-0.8x)^2+11.16<(0.5+0.8x)^2-0.25\\ 0.04-0.32x+0.64x^2+11.16<0.25+0.8x+0.64x^2-0.25\\ 0.64x^2-0.32x-0.64x^2-0.8x<-11.2\\-1.12x<-11.2\\x<10$