Question

(4(x + 1) >= 3(x + 3) - x,(2(2x - 1) > =7(x + 1)​

Answer 1

Ответ:

Пошаговое объяснение:

Если эта система неравенств, то решение такое:

4(x+1)≥3(x+3)-x; 4x+4≥2x+9; 4x-2x≥9-4; 2x≥5; x≥5/2; x≥2,5

2(2x-1)≥7(x+1); 4x-2≥7x+7; 4x-7x≤7+2; -3x≤9; x≤9/(-3); x≤-3

Тогда система неравенств не имеет решений.

Если же это отдельные два неравенства, тогда решение такое:

4(x+1)≥3(x+3)-x

4x+4≥2x+9

4x-2x≥9-4

2x≥5

x≥5/2

x≥2,5

x∈[2,5; +∞)

2(2x-1)≥7(x+1)

4x-2≥7x+7

4x-7x≤7+2

-3x≤9

x≤9/(-3)

x≤-3

x∈(-∞; -3]

Answer 2

To solve these inequalities, you'll need to isolate the variable, x, in each inequality. Here's how you can do that for each one:

1. Solve 4(x + 1) >= 3(x + 3) - x:

First, distribute the constants on the right side of the inequality:

4x + 4 >= 3x + 9 - x

Now, combine like terms:

4x + 4 >= 2x + 9

Subtract 2x from both sides:

4x - 2x + 4 >= 2x - 2x + 9

2x + 4 >= 9

Subtract 4 from both sides:

2x + 4 - 4 >= 9 - 4

2x >= 5

Now, divide by 2 (which is positive, so you don't need to flip the inequality sign):

2x/2 >= 5/2

x >= 5/2

So the solution to the first inequality is x >= 5/2.

2. Solve 2(2x - 1) >= 7(x + 1):

First, distribute the constants on both sides of the inequality:

4x - 2 >= 7x + 7

Now, move all terms containing x to one side and constants to the other side:

4x - 7x - 2 - 7 >= 7x - 7x + 7 - 7

-3x - 9 >= 0

Now, add 9 to both sides to isolate -3x:

-3x - 9 + 9 >= 0 + 9

-3x >= 9

Finally, divide by -3, remembering to reverse the inequality sign when dividing by a negative number:

(-3x)/(-3) <= 9/(-3)

x <= -3

So the solution to the second inequality is x <= -3.

Therefore, the solutions to the two inequalities are:

1. x >= 5/2
2. x <= -3