Question

2x – 6 ≥ 6(x – 2) + 8

Answer 1

2x - 6 ≥ 6(x - 2) + 8
2x - 6 ≥ 6x -12 +8
2x -6 ≥ 6x -4
     -6         -6
   2x ≥ 6x -10
 -6x    -6x
   -4x ≥ -10
     x < 2/5

Answer 2

2x - 6 > 6(x - 2) + 8
                                            use the distrubutive property
2x - 6 > 6x - 12 + 8
                                            combine like terms
2x - 6 > 6x - 4
                                    get "x" on one side by subtracting 6x from both sides
-4x - 6 > - 4 
add 6 to both sides so that you have x on one and actual numbers on the other
-4x >  2
  divide both sides by -4, and don't forget to flip the sign because you are dividing by a negative!!!!!

x < -0.5 or x < -1/2