Practice Questions

Inequalities and systems of inequalities

Difficulty: ★★☆

1308 • Задача 1, вариант 1

Solve the system of inequalities:

\[\left\{\begin{aligned}2x-2\ge x-8\\ -2x+7<-5\end{aligned}\right.\]

Your Answer:

\(x\in [-6;+\infty)\)

\(x\in (6;+\infty)\)

\(x\in [-6;6)\)

\(x\in (-\infty;6]\)

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Inequalities and systems of inequalities

Difficulty: ★★☆

1309 • Задача 1, вариант 2

Solve the inequality:

\[(2x-6)(x+1)<0\]

Your Answer:

\(x\in [-1;3]\)

\(x\in (-\infty;-1]\cup[3;+\infty)\)

\(x\in (-\infty;-1)\cup(3;+\infty)\)

\(x\in (-1;3)\)

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Inequalities and systems of inequalities

Difficulty: ★★☆

1310 • Задача 1, вариант 3

Solve the inequality:

\[-1\le -2x+3<5\]

Your Answer:

\(x\in [-1;2]\)

\(x\in (-1;2]\)

\(x\in (-\infty;-1]\cup(2;+\infty)\)

\(x\in [-1;2)\)

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Inequalities and systems of inequalities

Difficulty: ★★☆

1311 • Задача 1, вариант 4

Solve the inequality:

\[x^2+10x\ge 0\]

Your Answer:

\(x\in [-10;0]\)

\(x\in (-10;0)\)

\(x\in (-\infty;-10]\cup[0;+\infty)\)

\(x\in (-\infty;-10)\cup(0;+\infty)\)

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Inequalities and systems of inequalities

Difficulty: ★★☆

1312 • Задача 1, вариант 5

Solve the system of inequalities:

\[\left\{\begin{aligned}3x-5\ge x-15\\ -2x+1>-1\end{aligned}\right.\]

Your Answer:

\(x\in [-5;1]\)

\(x\in [-5;1)\)

\(x\in (-5;1]\)

\(x\in (-\infty;-5]\cup[1;+\infty)\)

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Inequalities and systems of inequalities

Difficulty: ★★☆

1313 • Задача 1, вариант 6

Solve the inequality:

\[(x-3)(4x+8)\ge 0\]

Your Answer:

\(x\in (-\infty;-2)\cup(3;+\infty)\)

\(x\in (-\infty;-2]\cup[3;+\infty)\)

\(x\in [-2;3]\)

\(x\in (-2;3)\)

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Inequalities and systems of inequalities

Difficulty: ★★☆

1314 • Задача 1, вариант 7

Solve the inequality:

\[-2\le -3x+4<16\]

Your Answer:

\(x\in [-4;2)\)

\(x\in (-4;2]\)

\(x\in (-\infty;-4]\cup(2;+\infty)\)

\(x\in [-4;2]\)

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Inequalities and systems of inequalities

Difficulty: ★★☆

1315 • Задача 1, вариант 8

Solve the inequality:

\[x^2-25<0\]

Your Answer:

\(x\in (-\infty;-5)\cup(5;+\infty)\)

\(x\in (-\infty;-5]\cup[5;+\infty)\)

\(x\in [-5;5]\)

\(x\in (-5;5)\)

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Inequalities and systems of inequalities

Difficulty: ★★☆

1316 • Задача 1, вариант 9

Solve the system of inequalities:

\[\left\{\begin{aligned}2x-4\ge x-10\\ -4x+1<-7\end{aligned}\right.\]

Your Answer:

\(x\in (-\infty;2]\)

\(x\in [-6;2]\)

\(x\in (2;+\infty)\)

\(x\in [-6;+\infty)\)

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Inequalities and systems of inequalities

Difficulty: ★★☆

1317 • Задача 1, вариант 10

Solve the inequality:

\[(5x-15)(x+4)<0\]

Your Answer:

\(x\in [-4;3]\)

\(x\in (-4;3)\)

\(x\in (-\infty;-4)\cup(3;+\infty)\)

\(x\in (-\infty;-4]\cup[3;+\infty)\)

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Inequalities and systems of inequalities

Difficulty: ★★☆

1318 • Задача 1, вариант 11

Solve the inequality:

\[-3\le -2x+7<13\]

Your Answer:

\(x\in (-\infty;-3]\cup(5;+\infty)\)

\(x\in [-3;5)\)

\(x\in [-3;5]\)

\(x\in (-3;5]\)

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Inequalities and systems of inequalities

Difficulty: ★★☆

1319 • Задача 1, вариант 12

Solve the inequality:

\[x^2-4x\le 0\]

Your Answer:

\(x\in (-\infty;0]\cup[4;+\infty)\)

\(x\in (0;4)\)

\(x\in [0;4]\)

\(x\in (-\infty;0)\cup(4;+\infty)\)

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Inequalities and systems of inequalities

Difficulty: ★★☆

1320 • Задача 1, вариант 13

Solve the system of inequalities:

\[\left\{\begin{aligned}3x-3\ge x-11\\ -2x+5>-7\end{aligned}\right.\]

Your Answer:

\(x\in [-4;6]\)

\(x\in (-4;6]\)

\(x\in (-\infty;-4]\cup[6;+\infty)\)

\(x\in [-4;6)\)

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Inequalities and systems of inequalities

Difficulty: ★★☆

1321 • Задача 1, вариант 14

Solve the inequality:

\[(x-6)(3x+12)\ge 0\]

Your Answer:

\(x\in (-\infty;-4]\cup[6;+\infty)\)

\(x\in [-4;6]\)

\(x\in (-4;6)\)

\(x\in (-\infty;-4)\cup(6;+\infty)\)

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Inequalities and systems of inequalities

Difficulty: ★★☆

1322 • Задача 1, вариант 15

Solve the inequality:

\[-5\le -3x+1<16\]

Your Answer:

\(x\in (-5;2]\)

\(x\in [-5;2]\)

\(x\in [-5;2)\)

\(x\in (-\infty;-5]\cup(2;+\infty)\)

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Inequalities and systems of inequalities

Difficulty: ★★☆

1323 • Задача 1, вариант 16

Solve the inequality:

\[x^2-49>0\]

Your Answer:

\(x\in [-7;7]\)

\(x\in (-\infty;-7]\cup[7;+\infty)\)

\(x\in (-7;7)\)

\(x\in (-\infty;-7)\cup(7;+\infty)\)

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Practice — Maths 9 • Inequalities and systems of inequalities

Inequalities and systems of inequalities

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Inequalities and systems of inequalities

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Inequalities and systems of inequalities

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Inequalities and systems of inequalities

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Inequalities and systems of inequalities

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Inequalities and systems of inequalities

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Inequalities and systems of inequalities

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Inequalities and systems of inequalities

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Inequalities and systems of inequalities

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Inequalities and systems of inequalities

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Inequalities and systems of inequalities

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Inequalities and systems of inequalities

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Inequalities and systems of inequalities

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Inequalities and systems of inequalities

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Inequalities and systems of inequalities

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Inequalities and systems of inequalities

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