Answer:
{[tex]x|x \: < \: - 4 \: or \: x \: > \: 4[/tex]}
Step-by-step explanation:
We want to solve the inequality:
[tex] - 2 |x| \: < \: - 8[/tex]
We divide through by -2 and reverse the inequality sign.
[tex] |x| \: > \: 4[/tex]
By definition of absolute value function:
[tex] - x \: > \:4 \: or \: x \: > \: 4[/tex]
We divide through by -1 in the first inequality and reverse the sign to get:
[tex]x \: < \: - 4 \: or \: x \: > \: 4[/tex]
