Question

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.

Answer 1

Answer:

- 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:

$c(a+b)=ac+bc\\\\c(a-b)=ac-bc$

2. The Addition property of equality states that:

$If\ a=b\ then\ a+c=b+c$

Then, given the equation:

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

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

$(4)(2a) + (4)(3)= (-3)(a) +(-3)(- 1) + 31 - 11a\\\\8a+12=-3a+3+31-11a$

After combining like terms, you can identify that the next  property he applied was the Addition property of equality, adding $14a$ to both sides of the equation:

$8a+12+(14)=-14a+34+(14)\\\\22a+12=34$