Question

Choose the correct description of the graph of the compound inequality

x − 2 > −4 and 3x less than or equal to 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

solve it you get x>-2
and 3x<=15
x<=5
so close on 5 open on -2
so C

Answer 2

C) A number line with an open circle on −2, a closed circle on 5, and shading in between

Step-by-step explanation

Remember that the symbols: < and > (read "less than" and "greater than" respectively) translates into an open circle in the number line.

The symbols: ≤ and ≥ (read "less or equal than" and "Greater or equal than" respectively) translates into a closed circle in the number line.

Now, let's solve each inequality:

`x-2>-4`

`x>-2` So we have an open circle on -2

3x less than or equal to 15

`3x\leq 15`

`x\leq (15)/(3)`

`x\leq 5` So we have a closed circle on 5

Our inequalities goes from -2 (open circle) to 5 (closed circle) on the number line.