What is the justification for each step in the solution of the equation?

54+2x=5x−3(2+6x)54+2x=5x−3(2+6x)

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54+2x=5x−3(2+6x)54+2x=5x−3(2+6x) Given
54+2x=5x−6−18x54+2x=5x−6−18x addition , division, multiplucation
54+2x=−13x−654+2x=−13x−6 multiplication, division, combine like terms
54=−15x−654=−15x−6 division , multiplication , subtraction
60=−15x60=−15x addition , multiplication, division
−4=x−4=x addition, division, subtraction