You can't put 'OR' into the field and get a solution.

What we suggest is that you first solve the first inequality '-6x-2>-14' and then the second '3x-8 <= -35'.

Since there is 'OR' between them the solution of  '-6x-2>-14' or '3x-8 <= -35' is the solution of '-6x-2>-14' U '3x-8 <= -35' ('U' stands for union)

Solution for '-6x-2>-14' is 

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Solution for '3x-8 <= -35' is

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The union of the 2 sets (-~, 2) and (-~, -9] is:

(-~, 2) U (-~, -9] = (-~, 2)

So, the solution for  '-6x-2>-14' or '3x-8 <= -35' is (-~, 2).

You might also want to check out 'Math expression entry' located here