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]

Ya i could just need to know what type of math