Solve out following inequalities.  Give both inequality & interval notation forms for the solution.

      -14 < -7 (3x + 2) < 1

Solution

-14 < -7 (3x + 2) < 1

-14< -21x -14 < 1

0 < -21x < 15

Don't get excited regarding the fact that one of the sides is zero now. It isn't a problem.  Again, as with the last part, we'll be dividing through a negative number and thus don't forget to switch the direction of the inequalities.

0 > x>  -15 /21

0 > x>  5/7       OR - 5/7

The interval notation of the solution is ( -5/7,0)