Question

For which value of a are all the solutions of 2(x-5)>3x+a less than or equal 5?

Answer 1

`2(x-5)>3x+a \\ 2x-10 > 3x+a \\ 2x-3x>a+10 \\ -x>a+10 \ \ \ |* (-1) \\ x<-a-10`

The solutions must be less than or equal to 5.

`-a-10 \leq 5 \\ -a \leq 5+10 \\ -a \leq 15 \ \ \ |* (-1) \\ a \geq -15`

All the solutions are less than or equal to 5 for a≥-15.