Is the equation 4x + 11 - 4 = 4x + 11 a conditional, contradiction, or identity?
Understand the Problem
The question is asking to identify the nature of the equation 4x + 11 - 4 = 4x + 11, specifically whether it is a conditional, contradiction, or identity statement.
Answer
The equation is a contradiction.
Answer for screen readers
The equation is a contradiction.
Steps to Solve
- Simplify the Equation
Start with the given equation:
$$ 4x + 11 - 4 = 4x + 11 $$
Combine like terms on the left side:
$$ 4x + 7 = 4x + 11 $$
- Isolate the Variable
Subtract $4x$ from both sides:
$$ 7 = 11 $$
- Analyze the Result
The statement $7 = 11$ is a false statement. It suggests that there are no values of $x$ that can satisfy the original equation.
- Classify the Equation
Since we arrived at a contradiction (a statement that is always false), we classify this as a contradiction.
The equation is a contradiction.
More Information
A contradiction occurs when two expressions cannot be true at the same time. When simplifying the equation led to a false statement, it indicated that no solution exists.
Tips
- Confusing an identity with a contradiction. An identity is true for all values of the variable, while a contradiction is false for all values.
- Not simplifying correctly, which can lead to incorrect classifications.
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