Question

Choose the correct description of the graph of the compound inequality

2x + 5 > 9 and 5x less than or equal to 30.

A) A number line with an open circle on 2, shading to the left, and a closed circle on 6, shading to the right
B) A number line with an open circle on 2, a closed circle on 6, and shading in between
C) A number line with a closed circle on 2, shading to the left, and an open circle on 6, shading to the right
D) A number line with a closed circle on 2, an open circle on 6, and shading in between

Answer 1

B) A number line with an open circle on 2, a closed circle on 6, and shading in between

Explanation:

easy answer

Answer 2

To do this, you first have to solve the first inequality for x: 2x+5>9, 2x>4 and x>2. Now solve the next one for x as well: 5x <=30, x<=6. Now work on putting them onto a number line together. Since there is not an "equal to" with that greater than, the circle is open above the 2. The next one has an "equal to" with it so that's a closed circle above the 6. This is a conjunction, meaning the solution will show what is shared between the 2 inequalities, so you have an open circle above the 2 and shading to the right til you get to the closed circle above the 6 (which is technically shaded to the left down to the open circle at 2). So your choice is B.