Madison created this solved this proof. she wants to know if she solved it correctly. after looking at the proof, decide whether she solved the proof correctly. if she did not explain why it is incorrect and correct it: given : 4(5n + 7)-3n = 3(4n - 9) prove: n=-11 statements reasons 4(5n + 7) - 3n = 3(4n - 9) given 20n + 28 - 3n = 12n - 27 distributive property 17n + 28 = 12n - 27 simplify 5n + 28 = -27 addition property of equality 5n = -55 multiplication property of equality n = -11 division property of equality

Given:    4(5 + 7) − 3 = 3(4 − 9)

Prove:        =    −11

Statement:

1.)  4(5   +   7) − 3 = 3(4 − 9) >   Given  

2.)  20 + 28 − 3 = 12 − 27  >  Distributive property of multiplication

3.)  Madison has >  17n   +   28 When she should have  >      used 17 − 39 = 12 − 27 Madison Simply instead she should have used  >   Subtraction

4.)  5 + 28    =    −27  she uses the Subtraction Property of Equality > She Should use >  Subtraction property of equality

5.)  5n      =    −55 Madison used the Multiplication Property of Equality > Instead of using the >  Subtraction property of equality

6.)    n  =     −11   >    Division property of equality  

Showing Work:

Simplifying

4(5n + 7) + -3n = 3(4n + -9)

Reorder the terms:

4(7 + 5n) + -3n = 3(4n + -9)

(7 * 4 + 5n * 4) + -3n = 3(4n + -9)

(28 + 20n) + -3n = 3(4n + -9)

Combine like terms:

20n + -3n = 17n

28 + 17n = 3(4n + -9)

Reorder the terms:

28 + 17n = 3(-9 + 4n)

28 + 17n = (-9 * 3 + 4n * 3)

28 + 17n = (-27 + 12n)

Solving

28 + 17n = -27 + 12n

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-12n' to each side of the equation.

28    +    17n     +     -12n    =     -27    +    12n    +   -12n

Combine like terms:

17n    +    -12n    = 5n

28    +    5n   =    -27    +    12n    +    -12n

Combine like terms:

12n + -12n = 0

28 + 5n = -27 + 0

28 + 5n = -27

Add '-28' to each side of the equation.

28 + -28 + 5n = -27 + -28

Combine like terms:

28 + -28 = 0

0 + 5n    =     -27     +     -28

5n     =     -27     +     -28

Combine like terms:

-27 + -28 = -55

5n     =     -55

Divide each side by '5'.

n     =    -11

Simplifying

n    =    -11

Hope that helps                            :)