Question

Solve the compound inequality: 3x+3>12 AND 6x+24<12

a)x>2 and x<−2
b)x<2 and x>−2
c)x>3 and x<−3
d)x<3 and x>−3

Answer 1

To solve the compound inequality 3x+3>12 AND 6x+24<12, solve each inequality separately and then find the values of x that satisfy both inequalities. The correct answer is x>3 and x<-2.

Step-by-step explanation:

To solve the compound inequality 3x+3>12 AND 6x+24<12, we need to solve each inequality separately and then find the values of x that satisfy both inequalities.

Solving the first inequality, 3x+3>12, we subtract 3 from both sides to get 3x>9. Then, divide both sides by 3 to get x>3.

Solving the second inequality, 6x+24<12, we subtract 24 from both sides to get 6x<-12. Then, divide both sides by 6 to get x<-2.

Since the solution needs to satisfy both inequalities, the correct answer is x>3 and x<-2, option a).