Solve the following inequality. 21<_-3(x - 4) < 30 A. 28<_x < 37 B. -3 <_ x < 6 C. -6 < x <_ -3 D. -10 < x <_ -3

Option C

Step-by-step explanation:

we have

The compound inequality can be divided into two inequality

-----> inequality A

----> inequality B

Solve inequality A

Divide by -3 both sides

when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol

Rewrite

The solution of the inequality A is the interval (-∞,-3]

Solve the inequality B

Divide by -3 both sides

when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol

The solution of the inequality B is the interval [-6,∞)

The solution of the compound inequality is

[-6,∞) ∩ (-∞,-3]=(-6,-3]