Answer:
Option B. {x | x < -12 or x > -6}
Step-by-step explanation:
we have
[tex]-\frac{2}{3}x>8[/tex] ---> inequality A
Solve for x
Multiply by -3/2 both sides
Remember that when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol
so
[tex]x < (-\frac{3}{2})8[/tex]
[tex]x < -12[/tex]
The solution of the inequality A is the interval (-∞,-12)
[tex]-\frac{2}{3}x<4[/tex] ----> inequality B
Solve for x
Multiply by -3/2 both sides
Remember that when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol
so
[tex]x > (-\frac{3}{2})4[/tex]
[tex]x >-6[/tex]
The solution of the inequality B is the interval (-6,∞)
therefore
The solution of the system
[tex]-\frac{2}{3}x>8[/tex] or [tex]-\frac{2}{3}x<4[/tex] is equal to
(-∞,-12) ∪ (-6,∞)
{x | x < -12 or x > -6}
