Question

Which of the following is the correct graph of the solution to the inequality −13 > −5x + 2 > −28?

Answer 1

what is open and what is closed?
My answer is 3<x<6 but now I'm stuck for the number line

Answer 2

3<x<6

3 < x # x is greater than 3, not =3 , but greater, so it doesn't include it, thus is open
x < 6 # x is less than 6, not = 6, just less than 6, so it doesn't include it, thus open too

Answer 3

−13 > −5x + 2 > −28

Re-write as:

-28 < -5x + 2 < -13

add 20.5 to each side:

-28 + 20.5 < -5x + 2 + 20.5 < -13 + 20.5
-7.5 < -5x + 22.5 < 7.5

|22.5 - 5x| < 7.5
|5x - 22.5| < 7.5

-7.5 < 5x - 22.5 < 7.5
-7.5 + 22.5 < 5x < 7.5 + 22.5
15 < 5x < 30
15/5 < x < 30/5
3 < x < 6