Question

Kelly wrote the following steps to prove the equation:

Given: 2(x – 3) = 5x + 3
Prove: x = –3

Step
Mathematical Statement
Justification
0
2(x - 3) = 5x + 3
Given
1
2x - 6 = 5x + 3
Distributive Property
2
– 6 = 3x + 3
Subtraction Property of Equality
3
3x + 3 = –6
Transitive Property of Equality
4
3x = –9
Subtraction Property of Equality
5
x = –3
Division Property of Equality

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

Answer 1

Step 4; Combine Like Terms
Step 1; Commutative Property of Multiplication
Step 2; Associative Property of Addition
Step 3; Symmetric Property of Equality

Answer 2

Step 3 is not the transitive property. It's the symmetric property.

Answer 3

The symmetric property says:

If \(x=y\), then \(y=x\).