Question

LeeAnn 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 :7y-84=2y+61 Prove: y= 29 Statements Reasons 7y-84=2y+61 Given 5y - 84 = 61 Subtraction Property of Equality 5y = 145 Subtraction Property of Equality y = 29 Division Property of Equality

A’Riana 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 : 3(5x+1)=13x+5 Prove: x= 1 Statements Reasons 3(5x + 1) = 13x +5 Given 15x + 3 = 13x + 5 Simplify 2x + 3 = 5 Subtraction Property of Equality 2x = 2 Subtraction Property of Equality x = 1 Division Property of Equality

Answer 1

a) LeeAnn did not solve the proof correctly.

b)A'Riana did not solve the proof correctly.

Explanation:

a) First she she used Subtraction property of equality by subtracting 2 to both sides of the equation, which is correct:

`-2y+7y-84=2y+61-2y`

`5y-84=61`

2. But she should have used Addition property of equality and not Subtraction property of equality, because she add 84 to both sides of the equation:

`5y-84+84=61+84\\5y=145` (Addition property of equality )

3. Then, she did it correctly and applied Division Property of Equality .

b) 1. A'riana did not solve the proof correctly because the some Reasons are not clear. You have the following expression:

`3(5x+1)=13x+5` (Addition property of equality)

2. She should have used "Distributive property over adition" and not "Simplify". Therefore:

`15x+3=13x+5` (Distributive property over adition)

3. The next statement reason is correct. She used Subtraction property of equality by subtracting 13x to both sides of the equation.

4. The next statement reason is correct. She used Subtraction property of equality by subtracting 3 to both sides of the equation.

5. The next statement reason is correct. She used Subtraction property of equality by dividing 2 to both sides of the equation.