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Chapter 3: Problem 17

Identify as an expression or an equation. $$8 x-9=7$$

Short Answer

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Equation

Step by step solution

01

Understand the Problem

You are given the mathematical sentence: \[8x - 9 = 7\]. The task is to identify whether this sentence is an expression or an equation.
02

Definition of Expression

An expression is a combination of numbers, variables, and operators (such as + or -) that represents a value. Expressions do not have an equal sign.
03

Definition of Equation

An equation is a mathematical statement that asserts the equality of two expressions. Equations always have an equal sign (=).
04

Identify the Given Mathematical Sentence

The given sentence is \[8x - 9 = 7\]. Notice that it includes an equal sign (=).
05

Conclusion

Since the given sentence includes an equal sign, it is therefore classified as an equation.

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Key Concepts

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

expressions
In mathematics, an expression is a combination of numbers, variables, and mathematical operators such as addition, subtraction, multiplication, and division. Examples of expressions include \(3x + 2\) and \(5 - y\). The important thing to remember about an expression is that it does not contain an equal sign (\=). This means that an expression doesn't show a relationship between two quantities, but rather just gives a way to represent a value. Expressions are like phrases in language; they do not make a complete statement by themselves.
equal sign
The equal sign (\=) is a fundamental symbol in mathematics. It shows that two quantities are the same. Think of it as a way of saying 'is equal to.' For example, in the equation \(2 + 3 = 5\), the equal sign indicates that the sum of 2 and 3 is the same as 5. When you see an equal sign in a mathematical sentence, it means you're dealing with an equation. The equal sign creates a balance, showing that the values on both sides are equivalent. Without it, you'd have an expression which is more like an incomplete statement.
mathematical sentences
A mathematical sentence is a statement that can be either true or false. These sentences can be equations or inequalities. An equation, such as \(4x - 5 = 11\), has an equal sign and shows that one expression is equal to another. An inequality, on the other hand, uses symbols like \(>\), \(<\), \(鈮), and \(鈮) to show that one expression is larger or smaller than the other. Equations and inequalities help us understand the relationships between different mathematical expressions. In the given exercise, \(8x - 9 = 7\), we've identified the sentence as an equation because it has an equal sign showing that \(8x - 9\) is equal to 7.

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Most popular questions from this chapter

Solve the equation. $$1=\frac{h}{-5}$$

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