Question

Given: 2x – 3(x – 5 + x) = 2x – 3

Prove: x = 3





What are the missing justification steps, in order?

Distributive Property, Associative Property of Addition, Combine Like Terms

Subtraction Property of Equality, Associative Property of Addition, Addition Property of Equality

Subtraction Property of Equality, Commutative Property of Addition, Addition Property of Equality

Distributive Property, Commutative Property of Addition, Combine Like Terms

Answer 1

Mathematical Statement

Justification

2x – 3(x - 5 + x) = 2x - 3

Given

2x – 3(x + x – 5) = 2x – 3

Commutative Property of Addition

2x – 3(2x – 5) = 2x – 3

Combine Like Terms

2x – 6x + 15 = 2x – 3



(2x – 6x) + 15 = 2x – 3



– 4x + 15 = 2x – 3



– 6x + 15 = – 3

Subtraction Property of Equality

– 6x = – 18

Subtraction Property of Equality

x = 3

Division Property of Equality

Answer 2

going from

2x – 3(2x – 5) = 2x – 3

to

2x – 6x + 15 = 2x – 3

what property are we using here?

Answer 3

Distributive ?

Answer 4

yes you got it

Answer 5

so the answer is either


Distributive Property, Associative Property of Addition, Combine Like Terms


OR

Distributive Property, Commutative Property of Addition, Combine Like Terms

Answer 6

since those are the only two that start with "distributive property"

Answer 7

going from

2x – 6x + 15 = 2x – 3

to

(2x – 6x) + 15 = 2x – 3

what is happening (which property are we using now)?

Answer 8

then associative property and then combine like terms

Answer 9

you got it

Answer 10

thank you thank you :)

Answer 11

you're welcome