I will mark Brainliest for the right answer.

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

54+2x=5x-3 (2+6x)

Select the Best option for each place with question marks. These are your choices.

1. Addition Property Of Equality

2. Division Property Of Equality

3. Subtraction Property Of Equality

54+2x=5x-3 (2+6x) Given

54+2x=5x-6-18x?

54+2x=-13x-6 Combine like terms

54=-15x-6 Subtraction Property of Equality

60=-15x?

-4=x?

1st?: Distribution Property

2nd?: Addition

3rd?: Division

In the second step, none of those properties are being used. That is the distributive property. When you have a number being multiplied by parentheses, and inside the parentheses is a variable, you can apply the multiple to each term in the parentheses. None of the given properties apply there.

In 60 = - 15x, the property being used there is the addition property of equality.

You are adding 6 to the right side, and so you're also adding it to the left side. Doing so does not skew the equation, and it still remains equal.

In the last part, - 4 = x, the division property of equality is being used.

If we divide both sides by the same amount, the equation remains equal.

Dividing x by - 15 isolates the variable and gives the solution.