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Chapter 2: Problem 34

Determine whether each statement is an expression or an equation. $$3(x+1)=9$$

Short Answer

Expert verified
The provided statement, '3(x + 1) = 9', is an equation.

Step by step solution

01

Identify the Components of the Mathematical Sentence

Look at the mathematical sentence given. Here, we have '3(x+1)=9'.
02

Check for an Equality Sign

Check if there is an equality sign. In our case, we can see there is an equals sign between '3(x + 1)' and '9'.
03

Make a Conclusion

Since there is an equals sign, this mathematical phrase is asserting that '3(x+1)' and '9' are equal to each other. This makes it an equation.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Algebra Expressions
An **algebra expression** is a combination of numbers, variables, and arithmetic operations like addition, subtraction, multiplication, and division. Unlike equations, algebra expressions do not include an equality sign. This means they do not express a complete mathematical sentence describing a relationship.

Here are some features of algebra expressions:
  • They can involve just numbers, like: \( 5 + 6 \)
  • They can include variables, such as: \( 3x + 4 \)
  • They do not include equality signs (\( = \))
Understanding algebra expressions is crucial because they form the building blocks of equations. When you add an equality sign to an expression, it can often become an equation providing a meaningful relation.
Equality Sign
The **equality sign** is a fundamental symbol in mathematics, denoted as \( = \). It signifies that the values on both sides are equal to each other. The presence of an equality sign is what differentiates equations from expressions. Understanding its role is essential for solving mathematical relationships because:
  • It forms the basis of an equation, indicating that two expressions hold the same value.
  • The equality sign allows us to balance equations by performing identical operations on both sides.
For instance, in the sentence \( 3(x+1)=9 \), the equality sign establishes that the expression on the left equals the number on the right. Recognizing and applying the equality sign correctly helps in solving for unknowns (like \( x \) in this equation).
Mathematical Statement
A **mathematical statement** is any sentence that expresses a complete idea in mathematics. These can either be equations or expressions. The presence or absence of an equality sign typically distinguishes between complete statements (equations) and fragmented thoughts (expressions).

Key points about mathematical statements include:
  • An expression does not qualify as a complete statement because it lacks an outcome or condition.
  • Equations are complete statements as they assert that two expressions are equal, forming a condition to satisfy.
The given expression \( 3(x+1)=9 \) is a mathematical statement of equality, making it an equation. Identifying whether a statement is complete (an equation) or incomplete (an expression) helps determine the problem-solving approach.

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