Question

Choose the correct description of the graph of the compound inequality.

X-2 > -4 and 3x ≤ 15?
A) A number line with an open circle on -2, shading to the left, and a closed circle on 5, shading to the right
B) A number line with a closed circle on -2, shading to the left, and an open circle on 5, shading to the right
C) A number line with an open circle on -2, a closed circle on 5, and shading in between
D) A number line with a closed circle on -2, an open circle on 5, and shading in between.

Answer 1

The graph of the compound inequality is a number line with a closed circle on -2, an open circle on 5, and shading in between.

Step-by-step explanation:

The correct description of the graph of the compound inequality X-2 > -4 and 3x ≤ 15 is option D) A number line with a closed circle on -2, an open circle on 5, and shading in between.

To graph this compound inequality, first graph the inequalities separately:

X-2 > -4 represents a line with a closed circle at -2 and shading to the right.

3x ≤ 15 represents a line with an open circle at 5 and shading to the left.

Then, combine the graphs by shading in the overlapping region between the closed circle on -2 and the open circle on 5.