Problem 9 Determine whether each of the fo... [FREE SOLUTION]

91影视

Chapter 1: Problem 9

Determine whether each of the following is an expression or an equation. \(-3 x+2-4=x\)

Short Answer

Expert verified

Equation

Step by step solution

Identify Expressions and Equations

To determine whether a mathematical statement is an expression or an equation, look for an equals sign ('=').

Inspect the Given Statement

Examine the provided statement -3x + 2 - 4 = x and check for an equals sign.

Conclusion

Since there is an equals sign in the given statement, it indicates a relationship between two expressions. Hence, the statement is an equation.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Understanding Expressions vs Equations

When diving into algebra, it is crucial to distinguish between expressions and equations.
An expression is a mathematical phrase that can contain numbers, variables, and operators (such as +, -, *, /). For example, \(-3x + 2\) or \(-3x + 2 - 4\) are expressions because they do not have an equals sign ('=') and do not make a statement of equality.
In contrast, an equation is a statement that two expressions are equal. It always includes an equals sign. For example, \-3x + 2 - 4 = x\ is an equation because we can see the equals sign that connects two expressions.
Understanding this distinction helps us approach and solve mathematical problems appropriately.

The Process of Solving Equations

Solving equations involves finding the value of the variable that makes the statement true. Here鈥檚 a breakdown of the process:

First, simplify both sides of the equation if necessary.
Next, use algebraic operations to isolate the variable.
Perform the same operations on both sides to maintain equality.

Let's apply this with our example \(-3x + 2 - 4 = x\):

Simplify both sides: \(-3x - 2 = x\).
Move all terms involving x to one side by adding \- x\ on both sides: \(-3x - x = 2\) simplifies to \(-4x = 2\).
To isolate x, divide both sides by \-4\: \(x = -\dfrac{2}{4} = -\dfrac{1}{2}\).

Therefore, \(-\dfrac{1}{2}\) is the solution to the equation.

Exploring Algebraic Terms

In algebra, terms are the building blocks of expressions and equations. Terms can be constants, variables, or a combination of both multiplied together.
Let's break down \(-3x + 2 - 4\) as an example:

\(-3x\) is a term consisting of a coefficient \(-3\) and a variable \('x'\).
\(2\) is a constant term.
\(-4\) is also a constant term.

In an equation such as \-3x + 2 - 4 = x\, we see terms on both sides of the equals sign, working together to form expressions that we solve equations with.
Understanding terms is crucial for simplifying expressions and solving equations effectively.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Determine whether each of the following is an expression or an equation. \(-3 x+2-4=x\)

Short Answer

Step by step solution

Identify Expressions and Equations

Inspect the Given Statement

Conclusion

Key Concepts

Understanding Expressions vs Equations

The Process of Solving Equations

Exploring Algebraic Terms

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Logic and Functions

Decision Maths

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.