Choose the correct description of the graph of the compound inequality

3x + 2 > 2 and 3x less than 6.

A number line with an open circle on 0, shading to the left, and a closed circle on 2, shading to the right.

A number line with a closed circle on 0, shading to the left, and an open circle on 2, shading to the right.

A number line with a closed circle on 0, an open circle on 2, and shading in between.

A number line with an open circle on 0, a closed circle on 2, and shading in between.

We are given with two inequalities

3x + 2 > 2 (eqn 1) 3x < - 6 (eqn 2)

in eqn 1, we transpose 2 to the right side, then3x > 0, x > 0in eqn 2, we divide the whole equation by 3, that is x<-2

Thus the domain is. D. A number line with an open circle on 0, a closed circle on 2, and shading in between.

The correct answer is:

A number line with an open circle on 0, an open circle on 2, and shading in between. (This was not listed as a choice.)

Explanation:

Our first inequality is 3x+2 > 2.

To solve this, first subtract 2 from each side:

3x+2-2 > 2-2

3x > 0

Divide both sides by 3:

3x/3 > 0/3

x > 0

The second equation is "3x less than 6." This translates to

3x < 6

Divide both sides by 3:

3x/3 < 6/3

x < 2

This makes our answer "x > 0 and x < 2." This can also be written as

0 < x < 2.

To graph this, draw a number line. The numbers must range so that 0 and 2 are on it.

Draw open circles on 0 and 2. The circles are open because the signs are strictly greater than and strictly less than; there is no "greater than or equal to" or "less than or equal to."

Since the numbers are greater than 0 and less than 2, this means the number line between them will be shaded.