Question

complete the proof.

given: (2(x + 3) - 4x = x)

prove: (x = 2)

statements
(2(x + 3) - 4x = x)
(2x + 6 - 4x = x)
(-2x + 6 = x)
(6 = 3x)
(2 = x)
(x = 2)

Explanation:

Identify the given proof step

The problem asks us to complete an algebraic proof. We need to find the reason for the first statement:
Statement: \(2(x + 3) - 4x = x\)

Analyze the given information

The problem statement starts with:
"Given: \(2(x + 3) - 4x = x\)"
Therefore, the first statement in the proof is the starting equation that is directly provided to us.

Determine the correct reason

Since this equation is given at the start of the problem, the justification for writing this statement is "Given".

Answer:

Complete the proof.

Given: \(2(x + 3) - 4x = x\)

Prove: \(x = 2\)

Statements	Reasons
\(2x + 6 - 4x = x\)	Distributive Property
\(-2x + 6 = x\)	Combine like terms
\(6 = 3x\)	Addition Property of Equality
\(2 = x\)	Division Property of Equality
\(x = 2\)	Symmetric Property of Equality