In the equation 3x + 5 = 11, what does the equals sign (=) signify?
Understand the Problem
The question is asking for the interpretation of the equals sign in the equation 3x + 5 = 11, specifically what the equals sign signifies in terms of values.
Answer
**b. That $3x + 5$ and $11$ represent the same value.**
Answer for screen readers
The correct answer is:
b. That $3x + 5$ and $11$ represent the same value.
Steps to Solve
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Understanding the Equation The equation $3x + 5 = 11$ shows that the left-hand side (LHS) and the right-hand side (RHS) are equal.
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Meaning of the Equals Sign The equals sign ($=$) indicates that the two sides of the equation represent the same value. Therefore, whatever the LHS evaluates to, it must equal the RHS.
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Analyzing the Options We need to evaluate the provided options to see which one accurately reflects the meaning of the equals sign.
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Identifying the Correct Statement The correct option should state that the expressions on both sides of the equals sign are equal or represent the same value.
The correct answer is:
b. That $3x + 5$ and $11$ represent the same value.
More Information
The equals sign in an equation signifies equivalence. In this case, it shows that the value of $3x + 5$ is exactly the same as $11$ when $x$ is calculated correctly. Unequal relations would be represented differently.
Tips
- Misunderstanding the Equals Sign: Some might think it indicates only a numeric value or might consider it as a variable. Remember, it signifies equivalence, not variable status.
- Confusion with Order: Failing to realize that both expressions must equal each other as a fundamental property of equations.
