What is the justification for each step in solving the inequality?

75x+35≥7 (11x+9) + 475x+35≥7 (11x+9) + 4

75x+35≥7 (11x+9) + 475x+35≥7 (11x+9) + 4

75x+35≥77x+63+475x+35≥77x+63+4

75x+35≥77x+6775x+35≥77x+67

-2x+35≥67-2x+35≥67 - 2x≥32-2x≥32

x≤-16x≤-16

75x+35≥7 (11x+9) + 475x+35≥7 (11x+9) + 4

75x+35≥77x+63+475x+35≥77x+63+4 [expand all blackets]

75x+35≥77x+6775x+35≥77x+67 [collect like terms]

-2x+35≥67-2x+35≥67 - 2x≥32-2x≥32 [subtract 77x through]

x≤-16x≤-16 [subtract 35 through and divide through by 2]