/*! 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 24 Solve and check each equation. $... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 24

Solve and check each equation. $$2 n=8$$

Short Answer

Expert verified
The short answer is: To solve the equation \(2n = 8\), we isolate n by dividing both sides of the equation by 2: \(n = \frac{8}{2} = 4\). To check our solution, we substitute \(n = 4\) back into the original equation: \(2n = 2(4) = 8\), which confirms the solution is correct. Thus, \(n=4\).

Step by step solution

01

Identify the equation

We are given the equation $$2n=8$$.
02

Isolate the variable n

In order to isolate n, we need to divide both sides of the equation by 2. This will give us the value of n: \[\frac{2n}{2} = \frac{8}{2}\]
03

Perform the division

By dividing both sides of the equation by 2, we get: \[n=4\]
04

Check the solution

To check our solution, we will substitute the value of n (n = 4) back into the original equation: \[2n=2(4)=8\] Since the left side of the equation is equal to the right side, our solution is correct: \[n=4\] So the solution to the equation $$2n=8$$ is \(n=4\).

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.

Solving Linear Equations
When solving linear equations, our aim is to find the value of the unknown variable that makes the equation true. Linear equations are typically in the form of \( ax + b = c \), where \( a \), \( b \), and \( c \) are constants, and \( x \) is the variable to solve for.
To solve such an equation, follow these steps:
  • Identify and understand the equation: Recognize the equation and ensure all similar terms are on respective sides. For example, with \( 2n = 8 \), we already have all terms appropriately placed.
  • Isolate the variable: Apply algebraic operations to get the variable by itself on one side of the equation, typically by adding, subtracting, multiplying, or dividing both sides. In \( 2n = 8 \), we divide both sides by 2 to isolate \( n \).
  • Solve for the variable: Perform the operations to find the value of the variable (\( n = 4 \) in our example).
This process helps in finding the specific value that satisfies the equation.
Algebra Basics
Algebra is the branch of mathematics that involves using symbols and letters to represent numbers and quantities in equations and expressions. Understanding the basics of algebra is crucial for solving equations effectively.
Here are some fundamental concepts you need to know:
  • Variables: Symbols (usually letters) that stand in for unknown values. In our example, \( n \) is a variable.
  • Constants: Known values that don鈥檛 change, such as the numbers 2 and 8 in the equation \( 2n = 8 \).
  • Operations: Basic arithmetic operations like addition, subtraction, multiplication, and division that help manipulate the equation to solve it.
  • Equation: A mathematical statement that asserts the equality of two expressions, like \( 2n = 8 \).
Building a strong foundation in these basics allows you to tackle more complex algebraic problems.
Checking Solutions
Once a solution for an equation is found, it's important to verify its correctness. Checking solutions ensures that the equation was solved accurately and the found value satisfies the equation.
Follow these steps to check your solution:
  • Substitute the solution: Replace the variable with the solved value back into the original equation. For \( n = 4 \), plug it into \( 2n = 8 \).
  • Perform the arithmetic: Carry out the operations to see if both sides of the equation are equal. With \( 2(4) = 8 \), the equation holds true.
  • Confirm equality: If the left and right sides of the equation match, the solution is correct. In this case, both sides equal 8, confirming that \( n = 4 \) is accurate.
Checking solutions prevents errors and increases confidence in your answers.

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 using the five "Steps for Solving Applied Problems." See Examples \(7-9\) Twice a number is \(-16 .\) Find the number.

Write an equation and solve. Use the five "Steps for Solving Word Problems." Five times the sum of two consecutive integers is two more than three times the larger integer. Find the integers.

Solve. A jet flying at an altitude of \(35,000\) ft passes over a small plane flying at \(10,000\) ft headed in the same direction. The jet is flying twice as fast as the small plane, and thirty minutes later they are 100 mi apart. Find the speed of each plane.

Solve each equation and check your answer. $$8-7(2-3 w)-9 w=4(5 w-1)-3 w-2$$

Solve using the five "Steps for Solving Applied Problems." See Examples \(7-9\) Three times a number is fifteen more than half the number. Find the number.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Calculus

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.