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

Answer:

The correct option is 2.

Step-by-step 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.