Question

(x-5)(x+5)-x(x+3)<x+1

(4-y)(y+4)+y(5+y)>6y-20

(x+2)(x-6)-(x-7)(x+7)<30-3x

 x(8-3x)+11<3(7-x)(7+x)+8

Answer 1

1. $(x-5)(x+5)-x(x+3) textless x+1$
$x^2-25-x^2-3x textless x+1$
$-26-4x textless 0$
$x textgreater -6.5$

Ответ: x∈(6.5;+∞)
2. $(4-y)(y+4)+y(5+y) textgreater 6y-20$
$16-y^2+5y+y^2 textgreater 6y-20$
$36-y textgreater 0$
$y textless 36$

Ответ: x∈(-∞;36)
3. $(x+2)(x-6)-(x-7)(x+7) textless 30-3x$
$x^2-4x-12-(x-7)(x+7)-30+3x textless 0$
$x^2-4x-12-(x^2-49)-30+3x textless 0$
$x^2-4x-12-x^2+49-30+3x textless 0$
$-4x-12+49-30+3x textless 0$
$-4x+37-30+3x textless 0$
$-4x+3x textless -7$
$-x textless -7$
$x textgreater 7$

Ответ: x∈(7;+∞)
4. $x(8-3x)+11 textless 3(7-x)(7+x)+8$
$8x-3x^2-3(7-x)(7+x) textless 8-11$
$-3x^2+8x-147+3x^2 textless -3$
$8x textless 144$
$x textless 18$

Ответ: x∈(-∞;18)