Question

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

a.y+4 <3x+1
b.y-1<3x-4
c.y+4<3x-1
d.y-4<3x-1

Answer 1

Answer: d.
`y-4<3x-1`.

Explanation:

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

Let's check all inequalities :

a.
`y+4 <3x+1`

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

`0+4 <3(0)+1`

`\Rightarrow\ 4 <1` , which is wrong.

So , The point (0,0) is not a solution for
`y+4 <3x+1`.

b.
`y-1<3x-4`

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

`0-1<3(0)-4`

`\Rightarrow\ -1<-4`

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<3x-4`.

c.
`y+4<3x-1`

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

`0+4<3(0)-1`

`4<-1` , which is wrong.

So , The point (0,0) is not a solution for
`y+4<3x-1`.

d.
`y-4<3x-1`

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

`0-4<3(0)-1`

`-4<-1`

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<3x-1`.

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