What are the inequalities y>2x+1, y<-2x+3 can someone teach me how to do this?

Question

a.(-4,-1)

B.(0,0)

C.(0,2)

D(1,1)

e(1,3)

f(-1,2)

Answer 1

Step1:

To graph the inequality y>2x+1, first graph the line y=2x+1

Since y>2x+1, The graph of y=2x+1 is dashed and is not included in the graph of y>2x+1.

The region is shaded in yellow.

Step2:

To graph the inequality y<-2x+3, first graph the line y=-2x+3

Since y<-2x+3, The graph of y=-2x+3 is dashed and is not included in the graph of y<-2x+3.

The region is shaded in red.


Step 3:

The solution includes the ordered pairs in the intersection of the graphs of y>2x+1 and y<-2x+3

Here, the intersection of the graphs is shaded.

The ordered pairs in this region are the solutions of the given inequality.


Step 4:

Locate the points on the coordinate plane and the ordered pairs 

A (-4, -1) C (0, 2) and F (-1,2) are the solutions of the given inequality.

Answer 2

Graph for the inequalities y > 2x  +1 and y < -2x + 3 is

A (-4, -1) C (0, 2) and F (-1,2) are falling in the common shaded region. So, these point are the solutions to the inequalities y > 2x  +1 and y < -2x + 3.

Answer 3

lets go through the options.

The inequalities are y > 2x + 1 and y < - 2x + 3.

(a). (- 4, - 1).

Let, (x, y) = (- 4, - 1).

Now, the inequalities are

- 1 > 2(- 4) + 1  and  - 1 < - 2(- 4) + 3

- 1 > - 8 + 1  and  - 1 < 8 + 3

- 1 > - 7  and  - 1 < 11

The above two statements are true.

So, (- 4, - 1) is the solution to the given inequalities.

(B). (0, 0).

0 > 2(0) + 1  and  0 < - 2(0) + 3

0 > 1  and  0 < 3

The first statement is false and the second statement is true.

So, (0, 0) is the not a solution to the given inequalities.

(C). (0, 2).

2 > 2(0) + 1  and  2 < - 2(0) + 3

2 > 1  and  2 < 3.

The above two statements are true.

So, (0, 2) is the solution to the given inequalities.

(D). (1, 1).

1 > 2(1) + 1  and  1 < - 2(1) + 3

1 > 3  and  1 < 1.

The above two statements are false.

So, (1, 1) is not a solution to the given inequalities.

(e). (1, 3).

3 > 2(1) + 1  and  3 < - 2(1) + 3

3 > 3  and  3 < 1.

The above two statements are false.

So, (1, 3) is not a solution to the given inequalities.

(f). (- 1, 2).

2 > 2(- 1) + 1  and  2 < - 2(- 1) + 3

2 > - 2 + 1  and  2 < 2 + 3

2 > - 1  and  2 < 5.

The above two statements are true.

So, (- 1, 2) is the solution to the given inequalities.

 

Therefore, the points a(- 4, - 1), C(0, 2), and f(- 1, 2) are the solution points of the given inequalities.