For this case we must indicate the solution set of the given inequalities:
![-6x + 14](https://tex.z-dn.net/?f=-6x%20%2B%2014%20%3C-28)
Subtracting 14 from both sides of the inequality we have:
![-6x](https://tex.z-dn.net/?f=-6x%20%3C-28-14%5C%5C-6x%20%3C-42)
Dividing by 6 on both sides of the inequality:
![-x](https://tex.z-dn.net/?f=-x%20%3C-%20%5Cfrac%20%7B42%7D%20%7B6%7D%5C%5C-x%20%3C-7)
We multiply by -1 on both sides, taking into account that the sense of inequality changes:
![x> 7](https://tex.z-dn.net/?f=x%3E%207)
Thus, the solution is given by all values of x greater than 7.
On the other hand we have:
![9x + 15](https://tex.z-dn.net/?f=9x%20%2B%2015%20%3C-12)
Subtracting 15 from both sides of the inequality we have:
![9x](https://tex.z-dn.net/?f=9x%20%3C-12-15%5C%5C9x%20%3C-27)
Dividing between 9 on both sides of the inequality we have:
![x](https://tex.z-dn.net/?f=x%20%3C-%20%5Cfrac%20%7B27%7D%20%7B9%7D%5C%5Cx%20%3C-3)
Thus, the solution is given by all values of x less than -3.
Finally, the solution set is:
(-∞, - 3) U (7,∞)
Answer:
(-∞, - 3) U (7,∞)