Question

Решите систему2+x<0 2x+1<0​

Answer 1

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Answer 2

To solve the system of inequalities, we need to find the values of x that satisfy both inequalities simultaneously. Let's solve them one by one:

1. 2 + x < 0: Subtract 2 from both sides: x < -2

2. 2x + 1 < 0: Subtract 1 from both sides: 2x < -1

Finally, divide both sides by 2. Since we're dividing by a negative number, the inequality sign flips: x > -1/2

Now, we need to find the values of x that satisfy both inequalities (i.e., the values of x that are simultaneously less than -2 and greater than -1/2). To do this, we'll find the intersection of the two solution sets:

The solution set for x < -2 is (-∞, -2). The solution set for x > -1/2 is (-1/2, ∞).

The intersection of these two sets is the set (-1/2, -2). This means that x must be between -1/2 and -2, exclusive of both endpoints, in order to satisfy both inequalities.

So, the solution for the system of inequalities is: -1/2 < x < -2.