Question

Select all of the ordered pairs below that satisfy the linear inequality y < 2x + 2.

Answer 1

The ordered pairs satisfying the inequality are (-1, -2) and (2, 4).

To determine which ordered pairs satisfy the linear inequality y < 2x + 2, we can substitute the x and y values into the inequality and check if it holds true.

1. For the ordered pair (-3, -6):

-6 < 2(-3) + 2

-6 < -4

This statement is false, so (-3, -6) does not satisfy the inequality.

2. For the ordered pair (3, 9):

9 < 2(3) + 2

9 < 8

This statement is false, so (3, 9) does not satisfy the inequality.

3. For the ordered pair (-1, -2):

-2 < 2(-1) + 2

-2 < 0

This statement is true, so (-1, -2) satisfies the inequality.

4. For the ordered pair (2, 4):

4 < 2(2) + 2

4 < 6

This statement is true, so (2, 4) satisfies the inequality.

5. For the ordered pair (-2, 1):

1 < 2(-2) + 2

1 < -2

This statement is false, so (-2, 1) does not satisfy the inequality.

6. For the ordered pair (0, 2):

2 < 2(0) + 2

2 < 2

This statement is false, so (0, 2) does not satisfy the inequality.

Therefore, the ordered pairs that satisfy the linear inequality y < 2x + 2 are (-1, -2) and (2, 4).

Answer 2

We will determine the ordered pairs that satisfy the inequality as follows:

*(-3, -6):

`-6<2(-3)+2\Rightarrow-6<-4`

This is true, so the first ordered pair satisfies it.

*(3, 9):

`9<2(3)+2\Rightarrow9<8`

This is false, so the second ordered pair does not satisfy the inequality.

*(-1, -2):

`-2<2(-1)+2\Rightarrow-2<0`

This is true, so the third ordered pair satisfies it.

*(2, 4):

`4<2(2)+2\Rightarrow4<6`

This is true, so the fourth ordered pair satisfies it.

*(-2, 1):

`1<2(-2)+2\Rightarrow1<-2`

This is false, so the fifth ordered pair does not satisfy the inequality.

*(0, 2):

`2<2(0)+2\Rightarrow2<2`

This is false, so the sixth ordered pair does not satisfy the inequaltity.