Question

3. Решите неравенство: а) 2(1-х)>х+3 б) 4х+7≤6х+1 в)6+х<3-2хг) 6х≥8х+1 д) 4(1+х)>х-2 е) 3(1-х)+2(2-2х)<0ПОЖАЛУЙСТА СРОЧНО НАДО!!!​

Answer 1

Ответ:

В решении.

Объяснение:

3. Решите неравенство:

а) 2(1 - х) > х + 3;

2 - 2х > x + 3

-2x - x > 3 - 2

-3x > 1

3x < -1   знак меняется при делении на минус;

x < -1/3;

Решения неравенства: х∈(-∞; -1/3).

Неравенство строгое, скобки круглые.

б) 4х + 7 ≤ 6х + 1;

4х - 6х <= 1 - 7

-2x <= -6

2x >= 6     знак меняется при делении на минус;

x >= 3;

Решения неравенства: х∈[3; +∞).

Неравенство нестрогое, скобка квадратная, а знаки бесконечности всегда под круглой скобкой.

в) 6 + х < 3 - 2х;

х + 2х < 3 - 6

3x < -3

x < -1;

Решения неравенства: х∈(-∞; -1).

Неравенство строгое, скобки круглые.

г) 6х ≥ 8х + 1;

6x - 8x >= 1

-2x >= 1

2x <= -1

x <= -0,5;

Решения неравенства: х∈(-∞; -0,5].

Неравенство нестрогое, скобка квадратная, а знаки бесконечности всегда под круглой скобкой.

д) 4(1 + х) > х - 2;

4 + 4x > x - 2

4x - x > -2 - 4

3x > -6

x > -2;

Решения неравенства: х∈(-2; +∞).

Неравенство строгое, скобки круглые.

е) 3(1 - х) + 2(2 - 2х) < 0;

3 - 3x + 4 - 4x < 0

-7x + 7 < 0

-7x < -7

7x > 7       знак меняется при делении на минус;

x > 1;

Решения неравенства: х∈(1; +∞).

Неравенство строгое, скобки круглые.

Answer 2

Solution to the inequalities:

a) To solve the inequality 2(1-x) > x + 3, we can start by distributing the 2 on the left side of the inequality:

2 - 2x > x + 3

Next, we can combine like terms by adding 2x to both sides:

2 > 3x + 3

Then, we can subtract 3 from both sides:

-1 > 3x

Finally, we divide both sides by 3, remembering to reverse the inequality sign since we are dividing by a negative number:

x < -1/3 [[1]]

b) To solve the inequality 4x + 7 ≤ 6x + 1, we can start by subtracting 4x from both sides:

7 ≤ 2x + 1

Next, we can subtract 1 from both sides:

6 ≤ 2x

Finally, we divide both sides by 2:

3 ≤ x [[2]]

c) To solve the inequality 6x < 3 - 2x, we can start by adding 2x to both sides:

8x < 3

Then, we divide both sides by 8:

x < 3/8 [[3]]

d) To solve the inequality 6x ≥ 8x + 1, we can start by subtracting 8x from both sides:

-2x ≥ 1

Next, we divide both sides by -2, remembering to reverse the inequality sign since we are dividing by a negative number:

x ≤ -1/2 [[4]]

e) To solve the inequality 4(1 + x) > x - 2, we can start by distributing the 4 on the left side of the inequality:

4 + 4x > x - 2

Next, we can subtract x from both sides:

3x > -6

Finally, we divide both sides by 3:

x > -2 [[5]]

f) To solve the inequality 3(1 - x) + 2(2 - 2x) < 0, we can start by simplifying the left side of the inequality:

3 - 3x + 4 - 4x < 0

Next, we combine like terms:

7 - 7x < 0

Then, we subtract 7 from both sides:

-7x < -7

Finally, we divide both sides by -7, remembering to reverse the inequality sign since we are dividing by a negative number:

x > 1 [[6]]

I hope this helps! Let me know if you have any further questions.