Question

1) [7+2x>5+x, [3x+2<8+x; 2) [1-0,5x<4-x, [9-2,8x>6-1,3x; 3) [0,4x-1<0,5x-1,7, [2,7x-10<0,9x-1; 4)[2,8x-17>=0,3x-4,5, [12,3x-16,6<=7,1x+19,8; решите систему неравенств

Answer 1

1) {х>-2 и х<3, тогда ответ -2<x<3
2) {х<6 и х<2, тогда ответ x<2
3) {х>7 и х<5, тогда ответ решений нет
4) {х>=5 и х<=7, тогда ответ 5<=x<=7

Answer 2

Solving the System of Inequalities

To solve the given system of inequalities, let's solve each pair of inequalities separately and then find the intersection of their solutions.

1) Solving 7 + 2x > 5 + x and 3x + 2 < 8 + x:

Starting with the first inequality: 7 + 2x > 5 + x

Subtracting x from both sides: 7 + x > 5

Subtracting 7 from both sides: x > -2

The solution to the first inequality is x > -2.

Moving on to the second inequality: 3x + 2 < 8 + x

Subtracting x from both sides: 3x - x < 8 - 2

Simplifying: 2x < 6

Dividing by 2: x < 3

The solution to the second inequality is x < 3.

Combining the solutions: The solutions to the first pair of inequalities are x > -2 and x < 3.

2) Solving 1 - 0.5x < 4 - x and 9 - 2.8x > 6 - 1.3x:

Starting with the first inequality: 1 - 0.5x < 4 - x

Adding 0.5x to both sides: 1 < 4 - 0.5x

Subtracting 4 from both sides: -3 < -0.5x

Dividing by -0.5 (note that dividing by a negative number reverses the inequality): 6 > x

The solution to the first inequality is x > 6.

Moving on to the second inequality: 9 - 2.8x > 6 - 1.3x

Adding 1.3x to both sides: 9 + 1.3x > 6 + 2.8x

Subtracting 6 from both sides: 3 + 1.3x > 2.8x

Subtracting 1.3x from both sides: 3 > 1.5x

Dividing by 1.5: 2 > x

The solution to the second inequality is x < 2.

Combining the solutions: The solutions to the second pair of inequalities are x > 6 and x < 2.

3) Solving 0.4x - 1 < 0.5x - 1.7 and 2.7x - 10 < 0.9x - 1:

Starting with the first inequality: 0.4x - 1 < 0.5x - 1.7

Adding 1 to both sides: 0.4x < 0.5x - 0.7

Subtracting 0.5x from both sides: -0.1x < -0.7

Dividing by -0.1 (note that dividing by a negative number reverses the inequality): x > 7

The solution to the first inequality is x > 7.

Moving on to the second inequality: 2.7x - 10 < 0.9x - 1

Adding 10 to both sides: 2.7x < 0.9x + 9

Subtracting 0.9x from both sides: 1.8x < 9

Dividing by 1.8: x < 5

The solution to the second inequality is x < 5.

Combining the solutions: The solutions to the third pair of inequalities are x > 7 and x < 5.

4) Solving 2.8x - 17 >= 0.3x - 4.5 and 12.3x - 16.6 <= 7.1x + 19.8:

Starting with the first inequality: 2.8x - 17 >= 0.3x - 4.5

Adding 17 to both sides: 2.8x >= 0.3x + 12.5

Subtracting 0.3x from both sides: 2.5x >= 12.5

Dividing by 2.5: x >= 5

The solution to the first inequality is x >= 5.

Moving on to the second inequality: 12.3x - 16.6 <= 7.1x + 19.8

Subtracting 7.1x from both sides: 5.2x - 16.6 <= 19.8

Adding 16.6 to both sides: 5.2x <= 36.4

Dividing by 5.2: x <= 7

The solution to the second inequality is x <= 7.

Combining the solutions: The solutions to the fourth pair of inequalities are x >= 5 and x <=