1. The given absolute value inequality is:
[tex] |x| \: > \: 5[/tex]
This implies that;
[tex] - x \: > \: 5 \: or \: x \: > \: 5[/tex]
We the first inequality by -1 and reverse the sign to get:
[tex]x \: < - \: 5 \: or \: x \: > \: 5[/tex]
The correct answer is
C. { x|x < -5 or x > 5}
2. The given inequality is:
[tex] |4x - 8| \: < \: 12[/tex]
This implies that,
[tex] - (4x - 8) \: < \: 12 \: or \: (4x - 8) \: < \: 12[/tex]
Divide through the first inequality by -1 and reverse the sign
[tex]4x - 8\: > \: - 12 \: or \: 4x - 8\: < \: 12[/tex]
Group similar terms:
[tex]4x \: > \: - 12 + 8 \: or \: 4x \: < \: 12 + 8[/tex]
Simplify:
[tex]4x \: > \: - 4\: or \: 4x \: < \: 20[/tex]
Divide both sides by 4
[tex]x \: > \: - 1\: or \: x \: < \: 5[/tex]
