Question

Яка з систем нерівностей має єдиний розв'язок? А) x >=-3; x<=-2 Б) x>-2; x<-3 B) x>-3; x<-3 Г) x>=-3; x<=-3 <=, >= менше/більше або дорівнює 0

Answer 1

System of Inequalities with a Unique Solution

A system of inequalities has a unique solution when the solution set consists of a single point or a single interval on the number line. In other words, there is only one value or range of values that satisfies all the given inequalities.

Let's analyze the options provided:

A) x >= -3; x <= -2

In this case, the two inequalities are contradictory. There is no value of x that can simultaneously be greater than or equal to -3 and less than or equal to -2. Therefore, this system of inequalities does not have a unique solution.

B) x > -2; x < -3

Similarly, these two inequalities are contradictory. There is no value of x that can be greater than -2 and less than -3 at the same time. Therefore, this system of inequalities does not have a unique solution.

C) x > -3; x < -3

Once again, these two inequalities are contradictory. There is no value of x that can be simultaneously greater than -3 and less than -3. Therefore, this system of inequalities does not have a unique solution.

D) x >= -3; x <= -3

In this case, both inequalities are satisfied when x is equal to -3. Therefore, this system of inequalities has a unique solution, which is x = -3.

To summarize, the only system of inequalities that has a unique solution is option D) x >= -3; x <= -3.

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