Determine whether the origin is included in the shaded region and whether the shaded region is above or below the line for the graph of the following inequality: y < two thirds x + 2

answers:
a. the origin is not included in the shaded region and the shaded area is above the line.

b. the origin is not included in the shaded region and the shaded area is below the line.

c. the origin is included in the shaded region and the shaded area is above the line.

d. the origin is included in the shaded region and the shaded area is below the line.

Option: D is correct.

Step-by-step explanation:

since we are given a inequality as:

Clearly from the graph of the following inequality we could see that the origin is included in the shaded region and the shaded area is below the line.

Also it could be seen that if we put the origin points i.e. (0,0) in the inequality than 0<2 and the condition is true and hence origin is included in the shaded area.

Hence, option D is true.

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3