Which of the following is the solution set of -2|x| < -8 -4 > x > 4 x x < -4 or x > 4

Question

Which of the following is the solution set of -2|x| < -8

x
-4 < x < 4
x

Answer 1

We can solve this inequality by dividing both sides by -2. However, since we are dividing by a negative number, we need to reverse the inequality:

-2|x| < -8

|x| > 4

This inequality is satisfied when x is less than -4 or greater than 4, since the absolute value of any number less than -4 or greater than 4 will be greater than 4.

Therefore, the solution set is:

x

Answer 2

`x`

Explanation:

−2|x| < −8 ↷

−2x > 8 −2x < −8

___ __ ___ ___

−2 −2 −2 −2

`-4 > x` OR
`4 < x`

Whenever you multiply\divide by a negative, you reverse the inequality symbol.

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