Question

Which points are solutions to the linear inequality y < 0.5x + 2? Check all that apply. (–3, –2)   (–2, 1) (–1, –2) (–1, 2) (1, –2) (1, 2)

Answer 1

We have to determine the solutions to the linear inequality
`y< 0.5x+2`

1. Let us check for the ordered pair (-3,-2)

`y<0.5x+2`

`-2<(0.5 * -3)+2`

`-2<0.5`

which is true.

Therefore, (-3,-2) is the solution to the given inequality.

2. Let us check for the ordered pair (-2,1)

`y<0.5x+2`

`1<(0.5 * -2)+2`

1 < 1 which is not true.

Therefore, (-2,1) is not a solution to the given inequality.

3. Let us check for the ordered pair (-1,-2)

`y<0.5x+2`

`-2<(0.5 * -1)+2`

`-2 < 1.5` which is true.

Therefore, (-1,-2) is a solution to the given inequality.

4. Let us check for the ordered pair (-1,2)

`y<0.5x+2`

`2<(0.5 * -1)+2`

`2 < 1.5` which is not true.

Therefore, (-1,2) is not a solution to the linear inequality.

5. Let us check for the ordered pair (1,-2)

`y<0.5x+2`

`-2<(0.5 * 1)+2`

-2 < 2.5 which is true.

Therefore, (1,-2) is a solution to the given inequality.

6. Let us check for the ordered pair (1,2)

`y<0.5x+2`

2 < 0.5+2

2< 2.5 which is true.

Therefore, (1,2) is a solution to the linear inequality.

Therefore, (-3,-2) , (-1,-2) , (1,-2) and (1,2) are the solutions to the given linear inequality.

Answer 2

A)
`(-3,-2)`

C)
`(-1,-2)`

E)
`(1,-2)`

F)
`(1,2)`

Explanation:

we have

`y<0.5x+2`

we know that

If a ordered pair is a solution of the inequality

then

the ordered pair must be satisfy the inequality

Verify

Point A)
`(-3,-2)`

Substitute the value of x and value of y in the inequality an compare

`-2<0.5(-3)+2`

`-2<0.5` -------> is true

The ordered pair
`(-3,-2)` is a solution of the inequality

Point B)
`(-2,1)`

Substitute the value of x and value of y in the inequality an compare

`1<0.5(-2)+2`

`1<1` -------> is not true

The ordered pair
`(-2,1)` is not a solution of the inequality

Point C)
`(-1,-2)`

Substitute the value of x and value of y in the inequality an compare

`-2<0.5(-1)+2`

`-2<1.5` -------> is true

The ordered pair
`(-1,-2)` is a solution of the inequality

Point D)
`(-1,2)`

Substitute the value of x and value of y in the inequality an compare

`2<0.5(-1)+2`

`2<1.5` -------> is not true

The ordered pair
`(-1,2)` is not a solution of the inequality

Point E)
`(1,-2)`

Substitute the value of x and value of y in the inequality an compare

`-2<0.5(1)+2`

`-2<2.5` -------> is true

The ordered pair
`(1,-2)` is a solution of the inequality

Point F)
`(1,2)`

Substitute the value of x and value of y in the inequality an compare

`2<0.5(1)+2`

`2<2.5` -------> is true

The ordered pair
`(1,2)` is a solution of the inequality