Question

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

{x | -4 > x > 4}

{x | -4 < x < 4}

{x | x < -4 or x > 4}

Answer 1

\[x >4.............or -x >4........x <-4......\]
a

Answer 2

funny i notice a and c say the same thing

Answer 3

See attached picture for a visual explanation.

Algebraic steps:
\[
\begin{align*}
-2|x|&<-8\\
-|x| & < -4\\
|x|&>4
\end{align*}
\]
Algebraic steps explained:
First step: Divide by 2
Second step: "multiply by negative 1" and FLIP THE INEQUALITY
Third step: understand that |x|>4 means two things:
Thing 1 is that x > 4 which means "x is greater than positive 4"
Thing 2 is that x < -4 which means "x is less than negative 4"

Answer 4

As far as I know, (a) and (c) do not say the same thing. -4 > x > 4 is asking for a number x which is simultaneously less than -4 and greater than +4. Such a number does not exist. Unless the new algebra curriculum is using unusual notation (which I wouldn't put it past curriculum developers to do...) I am almost certain (a) is not correct.