The point below that is a solution to the inequality is?

Question

The point below that is a solution to the inequality x- 2y < -2 is?

A: (-1, -4)

B: (1, 2)

C: (0, -2)

D (2, 2)

Could you also explain in the answer to help me understand this, thanks.

Answer 1

Substitute each ordered pair (x,y) into the inequality and check for truth...

 

A. (-1,-4):

    (-1)-2(-4)<-2....substitue for "x, y"

           -1+8<-2....simplify

                 7<-2....False, NOT a solution

 

B.  (1,2):

     1-2(2)<-2........substitue for "x, y"

          1-4<-2.......simplify

            -3<-2.......True, IS a solution

 

C.  (0,-2):

     0-2(-2)<-2......substitue for "x, y"

              4<-2......simplify, False, NOT a solution

 

D.  (2,2):

      2-2(2)<-2.......substitute for "x, y"

          2-4<-2.......simplify

            -2<-2.......False, NOT a solution

 

 

So choice "B", ordered pair (1,2) is a solution to the inequality "x-2y<-2"

 

 

Answer 2

Hello Whitney,

 

The simplest way to solve is to check for each point. You can stop once you get a solution, but I am going to check all four points just to be sure.

 

A: x = -1, y = -4

-1-2(-4) = -1+(-2)(-4) = -1+8 = 7

Since 7 is not smaller than -2, point A is not a solution to the inequality.

 

B: x = 1, y = 2

1-2(2) = 1-4 = -3

Since -3 is smaller than -2, point B is a solution to the inequality.

 

C: x = 0, y = -2

0-2(-2) = -2(-2) = 4

Since 4 is not smaller than -2, point C is not a solution to the inequality.

 

D: x = 2, y = 2

2-2(2) = 2-4 = -2

Since -2 is not smaller than -2, point D is not a solution to the inequality.

 

After checking all four points it is clear that B:(1,2) is the only point that makes the inequality true.