John was given the equation 4(2a + 3)= -3(a - 1) + 31 - 11. Some steps an their reasons have already been completed. State a property of numbers for each missing reason.

The steps required to solve 4(2a + 3)= -3(a - 1) + 31 - 11 are:

a   =   11

The given equation is:

4(2a  +  3) =  -  3(a  -  1) +  31  -  11

4(2a  +  3)  =  -3(a  -  1)  + 20      (Subtraction rule)

8a  +  12   =  -3a  +  3  +  20      (Distributive rule)

8a  +  3a     =  3  +   20  -  12     (Grouping like terms)

11a    =   11                 (Equality principle of addition)

a   =  11/11                 (Equality rule of division)

a   =   1                     (Answer)

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- Disitributive property.

- Addition property of equality.

Step-by-step explanation:

The complete exercise is attached.

For this exercise you need to remember the following properties:

1. The Distributive property states that:

2. The Addition property of equality states that:

Then, given the equation:

You can identify that the first property John used was the Distributive property:

After combining like terms, you can identify that the next  property he applied was the Addition property of equality, adding to both sides of the equation: