Question

I'm really stuck.....Could someone help me solve this....
Jose wrote the following steps to prove the equation:
Given: 4(x + 1) = 10x – 8
Prove: x = 2

0

4(x + 1) = 10x – 8

Given
-----
1

4x + 4 = 10x – 8

Distributive Property
----
2

4 = 6x – 8

Subtraction Property of Equality
---
3

12 = 6x

Addition Property of Equality
---
4

6x = 12

Symmetric Property of Equality
---
5

x = 2

Associative Property of Multiplication


Which step of justification is incorrect, and what should the justification for that step be to solve the equation?

Answer 1

Here are the answers:
Step 5; Division Property of Equality

Step 1; Commutative Property of Addition

Step 3; Subtraction Property of Equality

Step 2; Addition Property of Equality

Answer 2

@jim_thompson5910 could you help me out??

Answer 3

any ideas? or are you completely stuck?

Answer 4

Yes! I am in the middle between it being step 2 and step 5

Answer 5

because both make sense, well, to me. lol :DD

Answer 6

it's kinda hard to read, but is step 2 this one

4 = 6x – 8 Subtraction Property of Equality

Answer 7

yeah. and how would it be subtraction, if 8 is being added to both sides

Answer 8

notice how the 4x is gone from the left side

Answer 9

the 10x on the right side turned into 6x

so what happened?

Answer 10

mhhhhmmmm. i see so thats the subtraction.

Answer 11

yes exactly, you're subtracting 4x from both sides

Answer 12

so it would be step 5 because it isn't mentioned about the division to get the answer

Answer 13

so step 2 is valid

BUT

step 5 is NOT valid because you're actually using the division property of equality to divide both sides by 6 to isolate x

Answer 14

yes you got it

Answer 15

yes!! yay!! thank you! I was really stuck. thank you so much for making that so clear :DD

Answer 16

you're welcome, glad to be of help