(x-5)(x+5)-x(x+3)6y-20(x+2)(x-6)-(x-7)(x+7)

June 2022 1 8 Report

(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

Answers & Comments

maonang 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)

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