To analyze the statement "Seventeen is eight more than a number" and determine which responses are true, we can break down the elements of this statement.
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This is an expression because it is written as a complete sentence.
- False: An expression does not convey a complete thought with an equality; it lacks an equality sign.
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This is an equation because two expressions are set equal to each other.
- True: The statement can be translated into the equation: \( 17 = x + 8 \), where \( x \) represents "a number."
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“A number” is the constant.
- False: "A number" is a variable or unknown value, not a constant.
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The word “is” means equals.
- True: In mathematical language, "is" often represents an equality, which is the case here.
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This is an expression because there is no word meaning equals.
- False: As established, the statement does imply an equivalence using the word "is," which indicates that it is indeed an equation.
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The operation is addition.
- True: The phrase "eight more than a number" indicates the addition operation (the number plus eight).
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This is an equation because it is written as a complete sentence.
- False: While it is written as a complete sentence, it is the equality implied by "is" that makes it an equation.
Based on this analysis, the four true statements are:
- This is an equation because two expressions are set equal to each other.
- The word “is” means equals.
- The operation is addition.
- (None of the other more general statements about being complete sentences or the nature of constants apply.)
Therefore, the correct statements to check would be 2, 4, and 6. Since you specifically ask for four but only three are true based on the provided answers, please ensure there’s a correct understanding or expand the question as needed.
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