ГДЗ по Алгебре 9 Класс Дидактические материалы Вариант 2 Номер 25 Мерзляк, Полонский, Рабинович, Якир — Подробные Ответы

Решите неравенство:

1) \(4(x-3) > x + 6\);

2) \(0,8(8 — 8y) \leq 3,2 — 0,8(y — 7)\);

3) \((x-1)^2 > 3x + 34\);

4) \(2x(2x+1)-5(x^2-3x) < x(2 — x) + 8\);

5) \(x-5 > x+1, \frac{4}{8} > 2\);

6) \(x+4 > x+2 = 6, 54\);

7) \(5x-2 > 8-11-x, \frac{4}{5} > 10\);

8) \((x+4)(x-2) — (x + 5)(x + 3) \leq -8x\);

9) \((3x+1)^2 -(x+2)(4x — 1) > 5(x — 1)^2 + 7x\);

10) \(8x(5 + 12x) -(6x -1)(6x + 1) \geq 10x\).

\(4(x-3)>x+6\)
\(4x-12>x+6\)
\(4x-x>6+12\)
\(3x>18\)
\(x>\frac{18}{3}\)
\(x>6\)
\(x\in(6;+\infty)\)

\(0{,}3(8-3y)\leq3{,}2-0{,}8(y-7)\)
\(2{,}4-0{,}9y\leq3{,}2-0{,}8y+5{,}6\)
\(-0{,}9y+0{,}8y\leq3{,}2+5{,}6-2{,}4\)
\(-0{,}1y\leq6{,}4\)
\(y\geq-64\)
\(y\in[-64;+\infty)\)

\(\frac{5}{18}x-\frac{54}{18}x\geq\frac{20}{6}+\frac{1}{6}\)
\(\frac{-49}{18}x\geq\frac{21}{6}\)
\(x\leq\frac{21}{6}:(-\frac{49}{18})\)
\(x\leq-\frac{9}{7}\)
\(x\in(-\infty;-\frac{9}{7}]\)

\(2x(2x+1)-5(x^{2}-3x)<x(2-x)+3\)
\(4x^{2}+2x-5x^{2}+15x<2x-x^{2}+3\)
\(2x+15x-2x<3\)
\(15x<3\)
\(x<\frac{3}{15}\)
\(x<0{,}2\)
\(x\in(-\infty;0{,}2)\)

\(\frac{x-5}{4}-\frac{x+1}{3}>2\)
\(3(x-5)-4(x+1)>2\cdot12\)
\(3x-15-4x-4>24\)
\(-x>43\)
\(x<-43\)
\(x\in(-\infty;-43)\)

\(\frac{x+4}{3}-\frac{x+2}{6}\leq4\)
\(2(x+4)-(x+2)\leq24\)
\(2x+8-x-2\leq24\)
\(x+6\leq24\)
\(x\leq18\)
\(x\in(-\infty;18]\)

\(\frac{5x-2}{4}-\frac{3-x}{5}>\frac{1-x}{10}\)
\(5(5x-2)-4(3-x)>2(1-x)\)
\(25x-10-12+4x>2-2x\)
\(25x+4x+2x>2+10+12\)
\(31x>24\)
\(x>\frac{24}{31}\)
\(x\in(\frac{24}{31};+\infty)\)

\((x+4)(x-2)-(x+5)(x+3)\leq-8x\)
\(x^{2}-2x+4x-8-(x^{2}+3x+5x+15)\leq-8x\)
\(2x-8-(8x+15)\leq-8x\)
\(2x-8-15\leq-8x\)
\(2x-23\leq0\)
\(2x\leq23\)
\(x\leq\frac{23}{2}\)
\(x\leq11{,}5\)
\(x\in(-\infty;11{,}5]\)

\((3x+1)^{2}-(x+2)(4x-1)>5(x-1)^{2}+7x\)
\(9x^{2}+6x+1-(4x^{2}-x+8x-2)>5(x^{2}-2x+1)+7x\)
\(9x^{2}+6x+1-(4x^{2}+7x-2)>5x^{2}-10x+5+7x\)
\(5x^{2}-x+3>5x^{2}-3x+5\)
\(-x+3>-3x+5\)
\(2x>2\)
\(x>1\)
\(x\in(1;+\infty)\)

\(3x(5+12x)-(6x-1)(6x+1)\geq10x\)
\(15x+36x^{2}-(36x^{2}-1)\geq10x\)
\(15x+1\geq10x\)
\(15x-10x\geq-1\)
\(5x\geq-1\)
\(x\geq-\frac{1}{5}\)
\(x\geq-0{,}2\)
\(x\in[-0{,}2;+\infty)\)

1.
\(4(x-3)>x+6\)
\(4x-12>x+6\)
\(4x-x>6+12\)
\(3x>18\)
\(x>\frac{18}{3}\)
\(x>6\)
\(x\in(6;+\infty)\)

2.
\(0{,}3(8-3y)\leq3{,}2-0{,}8(y-7)\)
\(2{,}4-0{,}9y\leq3{,}2-0{,}8y+5{,}6\)
\(2{,}4-0{,}9y\leq8{,}8-0{,}8y\)
\(-0{,}9y+0{,}8y\leq8{,}8-2{,}4\)
\(-0{,}1y\leq6{,}4\)
\(y\geq-64\)
\(y\in[-64;+\infty)\)

3.
\((x-1)^{2}>3x+34\)
\(x^{2}-2x+1>3x+34\)
\(x^{2}-5x+1>34\)
\(x^{2}-5x-33>0\)
\(x_{1,2}=\frac{5\pm\sqrt{25+132}}{2}=\frac{5\pm\sqrt{157}}{2}\)
\(x\in(-\infty;\frac{5-\sqrt{157}}{2})\cup(\frac{5+\sqrt{157}}{2};+\infty)\)

4.
\(2x(2x+1)-5(x^{2}-3x)<x(2-x)+8\)
\(4x^{2}+2x-5x^{2}+15x<2x-x^{2}+8\)
\(4x^{2}-5x^{2}+x^{2}+2x+15x-2x<8\)
\(0x^{2}+15x<8\)
\(15x<8\)
\(x<\frac{8}{15}\)
\(x<0{,}53\)
\(x\in(-\infty;0{,}53)\)

5.
\(x-5>x+1\)
\(-5>1\)
\(\emptyset\)

6.
\(\frac{x+4}{3}-\frac{x+2}{6}\leq4\)
\(\frac{2(x+4)-(x+2)}{6}\leq4\)
\(2x+8-x-2\leq24\)
\(x+6\leq24\)
\(x\leq18\)
\(x\in(-\infty;18]\)

7.
\(\frac{5x-2}{4}-\frac{3-x}{5}>\frac{1-x}{10}\)
\(\frac{25x-10-12+4x}{20}>\frac{2-2x}{20}\)
\(25x-10-12+4x>2-2x\)
\(25x+4x+2x>10+12+2\)
\(31x>24\)
\(x>\frac{24}{31}\)
\(x\in(\frac{24}{31};+\infty)\)

8.
\((x+4)(x-2)-(x+5)(x+3)\leq-8x\)
\(x^{2}-2x+4x-8-(x^{2}+3x+5x+15)\leq-8x\)
\(x^{2}+2x-8-x^{2}-8x-15\leq-8x\)
\(2x-8x-8-15\leq-8x\)
\(-6x-23\leq-8x\)
\(2x\leq23\)
\(x\leq\frac{23}{2}\)
\(x\leq11{,}5\)
\(x\in(-\infty;11{,}5]\)

9.
\((3x+1)^{2}-(x+2)(4x-1)>5(x-1)^{2}+7x\)
\(9x^{2}+6x+1-(4x^{2}+8x-2)>5x^{2}-10x+5+7x\)
\(9x^{2}+6x+1-4x^{2}-8x+2>5x^{2}-3x+5\)
\(5x^{2}-2x+3>5x^{2}-3x+5\)
\(-2x+3>-3x+5\)
\(x>2\)
\(x\in(2;+\infty)\)

10.
\(3x(5+12x)-(6x-1)(6x+1)\geq10x\)
\(15x+36x^{2}-(36x^{2}-1)\geq10x\)
\(15x+1\geq10x\)
\(15x-10x\geq-1\)
\(5x\geq-1\)
\(x\geq-\frac{1}{5}\)
\(x\geq-0{,}2\)
\(x\in[-0{,}2;+\infty)\)