Question

Which of the following is a solution of the compound inequality -1 < 2n + 1 < 5? (Points : 2)
-1 < n < 5
n > 2 or n < -1
-1 < n < 2
n < -2 or n > 4

7. Which of the following is a solution of the compound inequality?
3x + 8 < 2 or x + 12 > 2 - x

(Points : 2)
x < -2 or x > 5
x < -6 and x > 5
All real numbers
No solution

Answer 1

thank you

Answer 2

you can select a number from each possible and test by substitution...

-1<n<5 pick n = 4 and substitute -1 < 2x4 + 1< 5 T or F

etc

or you can solve it using the balance method...

-1 < 2n + 1 < 5
-1 -1 -1

-2 < 2n < 4

divide by 2 -1 < n< 2

Answer 3

7. All real numbers
x < -2 or x > -5
The graph would be the entire number line.

http://www.wolframalpha.com/input/?i=3x+%2B+8+%3C+2+or+x+%2B+12+%3E+2+-+x