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Chapter 2: Problem 328

In the following exercises, determine if each is an expression or equation. $$ 10 x=120 $$

Short Answer

Expert verified
Equation

Step by step solution

01

Identify the components

Look at the given mathematical statement: $$10x = 120$$Identify whether there are terms separated by an equal sign or just mathematical expressions.
02

Check for an equal sign

Determine if there is an equal sign in the statement. An equation will have an equal sign, whereas an expression will not.
03

Classify the statement

Since the statement has an equal sign ($$10x = 120$$), it satisfies the criteria for being an equation.

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Key Concepts

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

Mathematical Expressions
In mathematics, we frequently encounter mathematical expressions. These are combinations of numbers, variables, and operations (like +, -, \times, 梅) that represent a value.

For example, consider the simple expression \(\text{3x + 5}\). This does not contain an equal sign, and we cannot determine a fixed value without knowing \text{x}.

Key characteristics of mathematical expressions include:
  • They do not have an equal sign.
  • They can be simplified but not solved.
  • They can contain numbers, variables, and operations.

Expressions help us make sense of quantities and relationships in algebra without needing to solve for a specific value.
Equations
Equations are vital in algebra. An equation is a statement that shows the equality of two expressions. This means that what is on the left side of the equal sign is the same as what is on the right side.

For instance, consider the equation given in the exercise: \(10x = 120\). Here, we have two expressions, \(10x\) and \(120\), that are claimed to be equal.

Important features of equations include:
  • They always have an equal sign.
  • They can be solved to find the value of the variable(s).
  • They represent a statement of equality between two mathematical expressions.

In the exercise, \(10x = 120\) is categorized as an equation because of the equal sign. Solving the equation would involve finding the value of \(x\) that makes this statement true.
Equal Sign
The equal sign ( \(=\) ) is a fundamental symbol in mathematics. It separates the left-hand side from the right-hand side in an equation, indicating that the two sides are of equal value.

Understanding the role of the equal sign is crucial for distinguishing between expressions and equations:
  • In expressions, there is no equal sign, so there is no assertion of equality.
  • In equations, the equal sign is what transforms a simple expression into an algebraic statement of equality.

For example, in our exercise statement \((10x=120)\), the equal sign shows that \(10x\) is equal to \(120\). This means we can solve for the value of \(x\). Without the equal sign, \(10x + 120\) would simply be an expression, not asserting any equality.

Always check for the equal sign when trying to classify a mathematical statement. It's the key to identifying equations!

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Most popular questions from this chapter

In the following exercises, list all the multiples less than 50 for each of the following. $$ 8 $$

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