Decide Whether the Equation Is an Identity, a Conditional Equation $$2 [ 3 - ( 6 - 5 x ) ] - x = - 12 + 3 ( 2 + 3 x )$$

question 359

Multiple Choice

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
- $$2 [ 3 - ( 6 - 5 x ) ] - x = - 12 + 3 ( 2 + 3 x )$$

• A) Identity; {all real numbers}
• B) Conditional; \(\{ - 6 \}\)
• C) Conditional; \(\{ 12 \}\)
• D) Contradiction; \(\varnothing\)

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Definitions:

Atomic Components

Fundamental parts or elements that cannot be broken down further into simpler constituents within a particular context or framework.

Tautological Consequent

A conclusion in a deductive argument that is true by definition or is logically unavoidable.

Tautology

A statement that is true in every possible interpretation, often repeating the same idea in different words unnecessarily.

Self-Contradictory Antecedent

A condition in a hypothetical statement that contradicts itself, making the statement impossible or illogical.