Question

What is the solution set of the compound inequality x+4<-3x+12<24

Answer 1

Hello! For these types of inequalities, we put what’s in the middle to solve for the one behind and ahead. -3x + 12 is in the middle. Let’s solve it like this: x + 4 < -3x + 12. Add 3x to both sides to get 4x + 4 < 12. Subtract 4 from both sides to get 4x < 8. Divide each side by 4 to isolate the “x”. 8/4 is 2. x < 2. Now, let’s solve the other like this: -3x + 12 < 24. Subtract 12 from both sides to get -3x < 12. Divide each side by -3 to isolate the “x”. 12/-3 is -4. Because you divided by a negative, you flip the sign over into greater than. The solution to the compound inequality is -4 < x < 2, but none of the choices show that. In this case, the part of the solution is x < 2, so if you had to pick from one of the answers, the answer is C.