Question

The point (0,0) is a solution to which of these inequalities?

Answer 1

Answer: d. $y-4$.

Step-by-step explanation:

To find : The point (0,0) is a solution to which of the given  inequalities.

Let's check all inequalities :

a.  $y+4$

Substitute (x,y) = (0,0) , we get

$0+4$

$\Rightarrow\ 4$ , which is wrong.

So , The point (0,0) is not a solution for $y+4$.

b.  $y-1$

Substitute (x,y) = (0,0) , we get

$0-1$

$\Rightarrow\ -1$

Multiply (-1) on both sides , we get

$1>4$  , which is wrong.

[Note : when we multiply a negative number to both sides of an inequality then the inequality sign gets reversed. ]

So , The point (0,0) is not a solution for $y-1$.

c. $y+4$

Substitute (x,y) = (0,0) , we get

$0+4$

$4$ , which is wrong.

So , The point (0,0) is not a solution for $y+4$.

d. $y-4$

Substitute (x,y) = (0,0) , we get

$0-4$

$-4$

Multiply (-1) on both sides , we get

$4>1$, which is correct.

[Note : when we multiply a negative number to both sides of an inequality then the inequality sign gets reversed. ]

So , The point (0,0) is a solution for $y-4$.

Answer 2

Let us test the four inequalities with the point (0,0).

a. y+4 < 3x + 1
Is 0 + 4 < 0 + 1 ? or 4 < 1 ?
NO

b. y - 1 < 3x - 4
Is 0 - 1 < 0 - 4 or -1 < -4 ?
NO

c. y + 4 < 3x - 1
Is 0 + 4 < 0 + 1 or 4 < 1 ?
NO

d. y - 4 < 3x - 1
Is 0 - 4 < 0 - 1 or -4 < -1 ?
YES

Answer:  d. y - 4 < 3x - 1