Question

Given: x – 2(x + 2 + 2x) = 10 + 2x
Prove: x = –2
Mathematical Statement Justification
x – 2(x + 2 + 2x) = 10 + 2x Given
x – 2(x + 2x + 2) = 10 + 2x Commutative Property of Addition
x – 2(3x + 2) = 10 + 2x Combine Like Terms
x – 6x – 4 = 10 + 2x Distributive Property
– 5x – 4 = 10 + 2x
– 7x – 4 = 10
– 7x = 14
x= –2 Division of Property Equality

What are the missing justification steps, in order?
Distributive Property, Addition Property of Equality, Subtraction Property of Equality
Combine Like Terms, Subtraction Property of Equality, Addition Property of Equality

Answer 1

The answers:
1. Distributive Property, Addition Property of Equality, Subtraction Property of Equality
2. Combine Like Terms, Subtraction Property of Equality, Addition Property of Equality
3. Distributive Property, Combine Like Terms, Subtraction Property of Equality
4. Combine Like Terms, Distributive Property, Addition Property of Equality

Answer 2

Mind helping me?

Answer 3

well what do they do with the x's in the first part

Answer 4

distributive property?

Answer 5

you can see that x-6x and then in the next it is -5x

Answer 6

okay.

Answer 7

distributive property is this : a(b+d)=ab+ad

Answer 8

oh is it combine like properties?

Answer 9

I mean terms

Answer 10

combine like terms, yes it is taking the x terms and making them one

Answer 11

alright I got that so far

Answer 12

subtraction property next?

Answer 13

yes because the 2x is positive on the right side and disappears in the next line

the subtraction property of equality says that you can subtract something from both sides and the equation will be equal still

Answer 14

So is the answer 2?

Answer 15

Don't see how it can be 4

Answer 16

yes lastly the addition property is saying that if you add the same number or term to each side, the answer will be the same... in this case they add 4 to both sides to get rid of the 4 on the left side

Answer 17

Mind helping me with one more?

Answer 18

sure post it

Answer 19

I can just put it in here right?

Answer 20

Nathan wrote the following steps to prove the equation:
Given: 3(x + 2) = 6x + 3
Prove: x = 1

Step Mathematical Statement Justification
0 3(x + 2) = 6x + 3 Given
1 3x + 6 = 6x + 3 Distributive Property
2 6 = 3x + 3 Commutative Property of Addition
3 3x + 3 = 6 Symmetric Property of Equality
4 3x = 3 Subtraction Property of Equality
5 x =1 Division Property of Equality

Which step of justification is incorrect, and what should the justification for that step be to solve the equation?
Step 4; Commutative Property of Multiplication
Step 1; Associative Property of Addition
Step 2; Subtraction Property of Equality
Step 3; Reflexive Property of Equality