Question

What are the justifications for each of the different steps

The options for each are
-Given
-Addition property of equality
-Multiplication property of equality
-Division property of equality
-Write an equivalent equation
-Distributive property

Answer 1

Step A : Given

Step B : Multiplication property of equality

Step C : Distributive Property

Step D : Write an equivalent equation

Step E : Addition property of equality

Step F : Division property of equality

Answer 2

Step A : -2.5(0.5 - 2.5x - 2.5) + 2.5(-4x -1) = -2x - 4 x

Given, is used in "given this equation"

Step B: -5 (1- 5) + 5( -8x - 2) = -4x - 8x

Here you can see like they multiplication both sides of the equation by 2.

2*( -2.5(0.5 - 2.5x - 2.5) + 2.5(-4x -1)) = 2*(-2x - 4 x)

-5(0.5 - 2.5x - 2.5) + 5(-4x -1) = -4x - 8 x

Looks like your teacher also multiplied by two inside the parentheses, which is a mistake, but we will keep progressing with the expressions in the image.

So the option here is multiplication property of equality.

Step C: Here you are solving the parentheses, this is the distributive property.

Step D: Now you are writing a equivalent equation, in this step you have:

-5 + 25x -40x - 10 = -4x - 12x

(-5 - 10) + (25x - 40x) = -12x

-15 - 15x = -12x

Step E: Here you are adding 15x in both sides of the equation, you are using the addition property of equality.

Step F: now you are dividing both sides by 3, this is the division property of equality.