Question

{(х-1) (х+3)+5>х(х-2)-14, {2(х+2,2)+х<-2х-2,1 Смотреть ответ Zombynella Zombynella Объяснение: (х-1) (х+3)+5>х(х-2)-14 2(х+2,2)+х< -2х-2,1 x²+3x-x-3+5>x²-2x-14 2x+4,4+x< -2x-2,1 2x+2x> -14-2 3x+2x<-2,1-4,4 4x> -16 5x< -6,5 x> -4 x< -1,3               -4<x< -1,3     Решение системы неравенств

Answer 1

To solve the system of inequalities, let's work on each inequality separately and then combine the results.

1. Solve the first inequality: (x - 1)(x + 3) + 5 > x(x - 2) - 14

Expand and simplify: x^2 + 3x - x - 3 + 5 > x^2 - 2x - 14

Combine like terms: x^2 + 2x + 2 > x^2 - 2x - 14

Now, move all terms to the left side: x^2 + 2x + 2 - x^2 + 2x + 14 > 0

Simplify further: 4x + 16 > 0

Now, isolate 'x': 4x > -16

Divide by 4 (since the coefficient is positive, the inequality sign does not change): x > -4

2. Solve the second inequality: 2(x + 2.2) + x < -2x - 2.1

Expand and simplify: 2x + 4.4 + x < -2x - 2.1

Combine like terms: 3x + 4.4 < -2x - 2.1

Now, move all terms to the left side: 3x + 2x + 4.4 + 2.1 < 0

Simplify further: 5x + 6.5 < 0

Now, isolate 'x': 5x < -6.5

Divide by 5 (since the coefficient is positive, the inequality sign does not change): x < -1.3

Now we have two inequalities:

1. x > -4
2. x < -1.3

To find the solution to the system, we need to find the overlapping region between the two inequalities, which is the intersection:

-4 < x < -1.3

So the solution to the system of inequalities is -4 < x < -1.3, meaning x must be greater than -4 and less than -1.3.