Respuesta :

The answer is (1, 1).

Graphing the equation you can see the points that lie on it.

or

[tex]y \geqslant |2x - 1| [/tex]
[tex]1 \geqslant |2(1) - 1| [/tex]
[tex]1 \geqslant |2 - 1| [/tex]
[tex]1 \geqslant |1| [/tex]
[tex]1 \geqslant 1[/tex]

Answer:

The correct option is 2.

Step-by-step explanation:

The given inequality is

[tex]y\geq |2x-1|[/tex]

If a point is part of the solution of the inequality, then the inequality must be satisfied by that point.

Check the inequality for (0,0),

[tex]0\geq |2(0)-1|[/tex]

[tex]0\geq |-1|[/tex]

[tex]0\geq 1[/tex]

This statement is false. So (0,0) is not a solution.

Check the inequality for (1,1),

[tex]1\geq |2(1)-1|[/tex]

[tex]1\geq |2-1|[/tex]

[tex]1\geq 1[/tex]

This statement is true. So (1,1) is a solution.

Check the inequality for (1,0),

[tex]0\geq |2(1)-1|[/tex]

[tex]0\geq |2-1|[/tex]

[tex]0\geq 1[/tex]

This statement is false. So (1,0) is not a solution.

Check the inequality for (3,2),

[tex]2\geq |2(3)-1|[/tex]

[tex]2\geq |6-1|[/tex]

[tex]2\geq 5[/tex]

This statement is false. So (3,2) is not a solution.

Therefore the correct option is 2.