Respuesta :
We have to determine the solutions to the linear inequality [tex] y< 0.5x+2 [/tex]
1. Let us check for the ordered pair (-3,-2)
[tex] y<0.5x+2 [/tex]
[tex] -2<(0.5 \times -3)+2 [/tex]
[tex] -2<0.5 [/tex]
which is true.
Therefore, (-3,-2) is the solution to the given inequality.
2. Let us check for the ordered pair (-2,1)
[tex] y<0.5x+2 [/tex]
[tex] 1<(0.5 \times -2)+2 [/tex]
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)
[tex] y<0.5x+2 [/tex]
[tex] -2<(0.5 \times -1)+2 [/tex]
[tex] -2 < 1.5 [/tex] which is true.
Therefore, (-1,-2) is a solution to the given inequality.
4. Let us check for the ordered pair (-1,2)
[tex] y<0.5x+2 [/tex]
[tex] 2<(0.5 \times -1)+2 [/tex]
[tex] 2 < 1.5 [/tex] 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)
[tex] y<0.5x+2 [/tex]
[tex] -2<(0.5 \times 1)+2 [/tex]
-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)
[tex] y<0.5x+2 [/tex]
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:
A) [tex](-3,-2)[/tex]
C) [tex](-1,-2)[/tex]
E) [tex](1,-2)[/tex]
F) [tex](1,2)[/tex]
Step-by-step explanation:
we have
[tex]y<0.5x+2[/tex]
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) [tex](-3,-2)[/tex]
Substitute the value of x and value of y in the inequality an compare
[tex]-2<0.5(-3)+2[/tex]
[tex]-2<0.5[/tex] -------> is true
The ordered pair [tex](-3,-2)[/tex] is a solution of the inequality
Point B) [tex](-2,1)[/tex]
Substitute the value of x and value of y in the inequality an compare
[tex]1<0.5(-2)+2[/tex]
[tex]1<1[/tex] -------> is not true
The ordered pair [tex](-2,1)[/tex] is not a solution of the inequality
Point C) [tex](-1,-2)[/tex]
Substitute the value of x and value of y in the inequality an compare
[tex]-2<0.5(-1)+2[/tex]
[tex]-2<1.5[/tex] -------> is true
The ordered pair [tex](-1,-2)[/tex] is a solution of the inequality
Point D) [tex](-1,2)[/tex]
Substitute the value of x and value of y in the inequality an compare
[tex]2<0.5(-1)+2[/tex]
[tex]2<1.5[/tex] -------> is not true
The ordered pair [tex](-1,2)[/tex] is not a solution of the inequality
Point E) [tex](1,-2)[/tex]
Substitute the value of x and value of y in the inequality an compare
[tex]-2<0.5(1)+2[/tex]
[tex]-2<2.5[/tex] -------> is true
The ordered pair [tex](1,-2)[/tex] is a solution of the inequality
Point F) [tex](1,2)[/tex]
Substitute the value of x and value of y in the inequality an compare
[tex]2<0.5(1)+2[/tex]
[tex]2<2.5[/tex] -------> is true
The ordered pair [tex](1,2)[/tex] is a solution of the inequality
