Question

Choose the correct solution.

- 2 l x l > - 8


a.
x < 4 and x > - 4


b.
x < 4 and x > - 4


c.
x < - 4 and x > 4


d.
x < - 4 and x > - 4

Answer 1

Answer: x < 4 and x > -4

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Work Shown:

-2 | x | > -8

| x | < -8/(-2)

| x | < 4

-4 < x < 4

-4 < x and x < 4

x < 4 and x < -4

x < 4 and x > -4

Side note: the inequality sign flips in the 2nd step because we divided both sides by a negative number. Also, I used the rule that
`| x | < k` leads to
`-k < x < k` only when k is positive.