Answer: d. [tex]y-4<3x-1[/tex].
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. [tex]y+4 <3x+1[/tex]
Substitute (x,y) = (0,0) , we get
[tex]0+4 <3(0)+1[/tex]
[tex]\Rightarrow\ 4 <1[/tex] , which is wrong.
So , The point (0,0) is not a solution for [tex]y+4 <3x+1[/tex].
b. [tex]y-1<3x-4[/tex]
Substitute (x,y) = (0,0) , we get
[tex]0-1<3(0)-4[/tex]
[tex]\Rightarrow\ -1<-4[/tex]
Multiply (-1) on both sides , we get
[tex]1>4[/tex] , 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 [tex]y-1<3x-4[/tex].
c. [tex]y+4<3x-1[/tex]
Substitute (x,y) = (0,0) , we get
[tex]0+4<3(0)-1[/tex]
[tex]4<-1[/tex] , which is wrong.
So , The point (0,0) is not a solution for [tex]y+4<3x-1[/tex].
d. [tex]y-4<3x-1[/tex]
Substitute (x,y) = (0,0) , we get
[tex]0-4<3(0)-1[/tex]
[tex]-4<-1[/tex]
Multiply (-1) on both sides , we get
[tex]4>1[/tex], 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 [tex]y-4<3x-1[/tex].
