/*! 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 7 Indicate whether each of the fol... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 7

Indicate whether each of the following is an expression or an equation. $$9+2(x+3)=14-x$$

Short Answer

Expert verified
Answer: The given statement is an equation.

Step by step solution

01

Analyze the given statement

The given statement is: $$9+2(x+3)=14-x$$. We can see there's an equal sign between two expressions, which means it connects two parts (left side and right side).
02

Identify the type of the given statement

Since there's an equal sign in the statement, which connects the left side and the right side, this indicates that it is an equation, rather than an expression.
03

Answer

The given statement $$9+2(x+3)=14-x$$ 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.

Mathematical Expressions
Mathematical expressions are like phrases in math. They consist of numbers, variables, and operators (such as addition, subtraction, multiplication, and division) that are combined to represent a value or a collection of terms. For example, in the expression \(9 + 2(x+3)\), we have:
  • The constant 9
  • The variable \(x\)
  • The multiplication of 2 with \((x+3)\)
Expressions do not have an equal sign. They simply represent a value or a relationship between variables and numbers on their own.
Think of expressions as the building blocks that can be used in equations. They help you convey mathematical ideas without asserting equality between two sides.
  • Example of an expression: \(4a + 7b - 5\)
  • Expressions can be simplified but not "solved" since they don't have an equal component.
Equal Sign
The equal sign is a fundamental symbol in mathematics, represented by \(=\). It serves as a bridge that connects two mathematical expressions, showing that they are equivalent in value. In the given problem, it plays a crucial role in defining the relationship between two sides of an equation:
  • In \(9+2(x+3) = 14-x\), the equal sign indicates that the expression on the left side is equal in value to the expression on the right side.
  • The equal sign demonstrates a balance between the two sides of the equation.
When you see an equal sign, you're witnessing a statement that points out the truthfulness of the equation as a whole. It's the claim that both halves have the same value once variables and operations are resolved.
The equal sign is what distinguishes an equation from a simple expression, by introducing a claim of balance or equivalency.
Expression vs Equation
Let's compare expressions and equations, and see where their differences lie.
An expression represents a mathematical phrase that can include numbers, variables, and operations, but it lacks an equal sign. This means it doesn't make a claim about equality.
  • Example: \(3y + 6\)
  • Purpose: It conveys a calculation or value.
A key feature of an equation, on the other hand, is that it contains an equal sign. It stands as a statement asserting that two expressions are equal in value. This characteristic is pivotal in solving or proving relationships:
In our original problem \(9+2(x+3)=14-x\):
  • "9+2(x+3)" is an expression.
  • "14-x" is another expression.
  • The equal sign between them forms an equation.
An equation, therefore, is a complete statement that you can solve, unlike expressions, which you simply evaluate or manipulate.

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

Find the GCF using prime factorization. 140 and 196

Factor. $$15 a^{2} b^{5}+25 a^{2} b^{3}-30 a^{2} b^{2}$$

State the conjugate of each binomial. $$-b+2$$

Simplify and write the resulting polynomial in descending order of degree. $$-9 c^{2}+c+4 c^{2}-5 c$$

For Exercises, find the GCF of the monomials. \(36 m^{5}, 48 m^{4},\) and \(60 m^{6}\)
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

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.