/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 8 Decide whether each of the follo... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 8

Decide whether each of the following is an expression or an equation. $$ 4(x+3)-2(x+1)+10 $$

Short Answer

Expert verified
Expression

Step by step solution

01

Understand the Difference Between Expression and Equation

An expression is a combination of numbers, variables, and operations without an equality sign. An equation includes an equality sign and shows that two expressions are equal.
02

Identify Components

Look at the given sequence: \[4(x+3)-2(x+1)+10\] Observe if there is an '=' sign that separates two expressions.
03

Determine If It鈥檚 an Expression or Equation

Since \[4(x+3)-2(x+1)+10\] doesn't have an equality sign ('='), it does not equate two expressions. This makes it an expression.

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 Algebraic Expressions
Algebraic expressions are fundamental in algebra. They are combinations of numbers, variables, and operations like addition, subtraction, multiplication, and division. What makes algebraic expressions unique is that they do not contain an equality sign '='. For example, in the expression \(4(x+3)-2(x+1)+10\), we see numbers, variables, and operations mixed together.
You can think of an algebraic expression as a mathematical phrase. It can be simplified but not solved in the traditional sense because it doesn't set one part equal to another. Simplifying expressions involves combining like terms and applying arithmetic operations. Here鈥檚 why it鈥檚 important:
  • They represent real-life quantities.
  • Can be part of larger equations or formulas.
  • Useful in problem-solving and mathematical modeling.
Exploring Algebraic Equations
Unlike expressions, algebraic equations include an equality sign (鈥�=鈥�), indicating that two expressions are equal. This means equations can be solved to find the value of the variables. An equation expresses a balance; something like \(4(x+3)-2(x+1)+10 = 20\) means both sides are equal.
Equations are vital because they allow us to solve for unknowns. In real life, equations can model relationships and changes in different variables. Understanding equations involves:
  • Identifying the parts of the equation.
  • Using various methods to isolate the variable.
  • Checking the solutions to ensure they are correct.
Identifying Algebra Components
Knowing the components of algebraic expressions and equations is crucial for understanding and solving them. Let鈥檚 break down the key components:
  • Variables: Symbols (often letters) representing unknown quantities. In the expression \(4(x+3)-2(x+1)+10\), 鈥榵鈥� is the variable.
  • Coefficients: Numbers multiplying the variables, such as 鈥�4鈥� and 鈥�2鈥� in the expression \(4(x+3)-2(x+1)+10\).
  • Terms: Individual parts separated by '+' or '-' signs. 鈥�4(x+3)鈥� and 鈥�-2(x+1)鈥� are terms in the given expression.
  • Operators: Signs indicating mathematical operations like addition (+), subtraction (-), multiplication (*), and division (/).
  • Constants: Numbers without variables, like 鈥�10鈥� in the expression \(4(x+3)-2(x+1)+10\).
Identifying these components helps in 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

Most popular questions from this chapter

Solve each problem about percent increase or percent decrease. Between 2000 and 2007 , the estimated population of Anchorage, Alaska, grew from \(320,391\) to \(362,340 .\) What was the percent increase to the nearest tenth?

Let \(A=\\{1,2,3,4,5,6\\}, B=\\{1,3,5\\}, C=\\{1,6\\}\) and \(D=\\{4\\} .\) Specify each set. See Examples I and 5. $$ A \cap D $$

Why is it impossible to mix candy worth \(\$ 4\) per lb and candy worth \(\$ 5\) per lb to obtain a final mixture worth \(\$ 6\) per Ib \(?\)

Decide whether each statement is true or false. If it is false, explain why. The union of the solution sets of \(x+1=6, x+1<6,\) and \(x+1>6\) is \((-\infty, \infty)\)

Jennifer Siegel invested some money at \(4.5 \%\) simple interest and \(\$ 1000\) less than twice this amount at \(3 \% .\) Her total annual income from the interest was \(\$ 1020 .\) How much was invested at each rate?
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.