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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.

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luisejr77

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:

[tex]c(a+b)=ac+bc\\\\c(a-b)=ac-bc[/tex]

2. The Addition property of equality states that:

[tex]If\ a=b\ then\ a+c=b+c[/tex]

Then, given the equation:

[tex]4(2a + 3)= -3(a - 1) + 31 - 11a[/tex]

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

[tex](4)(2a) + (4)(3)= (-3)(a) +(-3)(- 1) + 31 - 11a\\\\8a+12=-3a+3+31-11a[/tex]

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

[tex]8a+12+(14)=-14a+34+(14)\\\\22a+12=34[/tex]

Ver imagen luisejr77

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

  • Subtraction rule
  • Division rule
  • Distributive rule
  • Grouping like terms
  • Equality principle of addition
  • Equality rule of division

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)

Learn more here: https://brainly.com/question/14872729

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