Question

The opposite of one third of a number, x, decreased by 2 is greater than 2 and less than 8. What are the possible solutions?

Answer 1

So this is our inequality: $2<-\frac{1}{3}x-2<8$

Firstly, add 2 to all sides of the inequality: $4<-\frac{1}{3}x<10$

Next, multiply all sides of the inequality by -3, and since we are multiplying by a negative number flip the signs, and your answer will be: $-12>x>-30$