solve using addition and multiplication principles

Did I do this correct? Its been about 10 years since i been to school and am having some issues remembering how to do a lot of this stuff.

-6r-6 is less than or = to -2(2r-4)

my work below:

step 1: -6r-6 < or = to -4r+8

step 2: -6+4r < or = to 8+6

step 3: -2r < or = to 14/2

step 4: -2r div -2r < or = to 7

Answer: r > or = -7

Let me know if i did this correct sorry i dont know how to type the correct characters for less than or = to or divide etc.

Thanks in advance

Mr.H