/*! 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 67 Solve each equation. Check your ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 67

Solve each equation. Check your solution. $$ x+3=2 $$

Short Answer

Expert verified
The solution is \( x = -1 \).

Step by step solution

01

Isolate the Variable

We need to solve for the variable \( x \) in the equation \( x + 3 = 2 \). Start by isolating \( x \) on one side of the equation. To do this, subtract 3 from both sides of the equation:\( x + 3 - 3 = 2 - 3 \)This simplifies to:\( x = -1 \)
02

Check the Solution

Now that we have found a value for \( x \), we need to check our solution by substituting \( x = -1 \) back into the original equation to ensure both sides balance:\( (-1) + 3 = 2 \)This simplifies to:\( 2 = 2 \)Since both sides of the equation are equal, our solution \( x = -1 \) is correct.

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.

Isolating the Variable in Linear Equations
When solving linear equations, the main goal is to isolate the variable, typically represented by letters like \( x \). By isolating, we make sure one side of the equation solely contains the variable while the other side has all constants or numbers. This is crucial for finding the value of the variable.

Let's break down the steps:
  • Identify the term containing the variable. In the exercise given, this is \( x + 3 \).
  • To neatly "isolate" \( x \), you need to undo whatever operation is being done to it. Here, 3 is being added to \( x \). To undo this, you subtract 3 from both sides of the equation.
  • Mathematically, this looks as follows: \( x + 3 - 3 = 2 - 3 \). Simplifying gives you \( x = -1 \).

By performing the opposite operation on both sides, you ensure the equation remains balanced, leading you to the solution.
Checking Solutions in Algebra
After finding a potential solution for the variable, it's critical to check your work. This ensures that no errors were made in the process of solving the equation.

Here's how you can check your solution:
  • Substitute the found value back into the original equation. For this exercise, substitute \( x = -1 \) into \( x + 3 = 2 \).
  • Perform the calculations: Substituting \( -1 \) gives \( (-1) + 3 \), which should equal 2.
  • If both sides of the equation are equal, as \( 2 = 2 \), your solution is verified as correct.

Checking your solution essentially acts as a safeguard, confirming that you haven鈥檛 made any arithmetic mistakes. It鈥檚 a vital step in the problem-solving process!
Understanding Basic Algebra Concepts
Basic algebra involves understanding the rules and operations that allow us to manipulate equations to find variable values. Often these equations will have one or more operations that must be undone in a systematic way. In the provided exercise, the operation is addition, which is undone by subtraction.

Key essentials of basic algebra include:
  • Operations: Involve addition, subtraction, multiplication, and division.
  • Variables: Symbols like \( x \) represent numbers we aim to find.
  • Equations: Mathematical statements that show equality, such as \( x + 3 = 2 \).
  • Balancing: What you do to one side of the equation, you must do to the other to keep it balanced.

By familiarizing yourself with these concepts, you'll gain a solid foundation in basic algebra, making more complex topics easier to approach.

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

Graph each function. Identify the domain and range. \(h(x)=-3[x]\)

For which function is the range \(\\{y | y \leq 0\\} ?\) F. \(f(x)=-x\) G. \(f(x)=[x]\) H. \(f(x)=|x|\) J. \(f(x)=-|x|\)

Solve each inequality. (lessons \(1-5\) and \(1-6 )\) $$ |5-m| < 1 $$

Graph each function. Identify the domain and range. \(h(x)=|x+3|\)

Graph each function. Identify the domain and range. $$ h(x)=|x-3| $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Mechanics 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.