Question

Which point is part of the solution of the inequality y ≥ |2x − 1|.

(0, 0)


(1, 1)


(1, 0)


(3, 2)

Answer 1

The answer is (1, 1).

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

or


`y \geqslant |2x - 1|`

`1 \geqslant |2(1) - 1|`

`1 \geqslant |2 - 1|`

`1 \geqslant |1|`

`1 \geqslant 1`

Answer 2

The correct option is 2.

Explanation:

The given inequality is

`y\geq |2x-1|`

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),

`0\geq |2(0)-1|`

`0\geq |-1|`

`0\geq 1`

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

Check the inequality for (1,1),

`1\geq |2(1)-1|`

`1\geq |2-1|`

`1\geq 1`

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

Check the inequality for (1,0),

`0\geq |2(1)-1|`

`0\geq |2-1|`

`0\geq 1`

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

Check the inequality for (3,2),

`2\geq |2(3)-1|`

`2\geq |6-1|`

`2\geq 5`

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

Therefore the correct option is 2.