/*! 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 96 Find a solution for equation. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 96

Find a solution for equation. \(6=1 \cdot n\)

Short Answer

Expert verified
\(n = 6\)

Step by step solution

01

Understand the Equation

The given equation is \(6 = 1 \cdot n\). This equation states that 6 is equal to 1 multiplied by some variable \(n\). Our task is to find the value of \(n\) that satisfies this equation.
02

Isolate the Variable

To find the value of \(n\), we need to isolate it on one side of the equation. Since \(n\) is being multiplied by 1, we can simplify the equation directly to \(n = 6\).

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 Equations
At the heart of solving equations is finding the value of the unknown variable that makes the equation true. Think of an equation as a balanced scale. Whatever you do to one side, you must do to the other to keep it balanced. In the example equation, \(6 = 1 \cdot n\), we are trying to determine what \(n\) must be to make both sides equal.
Solving equations often involves a few consistent steps:
  • Understand the components of the equation: Identify the constants (numbers) and the variables (unknowns).
  • Determine what mathematical operations are being used: Are the variables being added, subtracted, multiplied, or divided?
  • Decide on the steps needed to find the unknown variable: This often involves reversing the order of operations.
In our exercise, understanding that \(n\) is simply replaced by the same operation doesn't require extensive rearranging, but the principles remain the same for more complex equations.
Isolating Variables
To solve an equation, isolating the variable is a critical step. This means getting the variable by itself on one side of the equation. This process helps us easily identify what number or expression the variable is equal to.
In the equation \(6 = 1 \cdot n\), \(n\) is being multiplied by 1. Since multiplying by 1 doesn't change the value, \(n\) is already isolated: \(n = 6\). In this scenario, isolating the variable is straightforward.
However, for more complex equations, isolating might involve:
  • Adding or subtracting numbers on both sides to clear things around the variable.
  • Multiplying or dividing to remove coefficients (numbers in front of variables).
  • Using inverse operations to move terms from one side of the equation to the other.
In every case, the goal is to manipulate the equation until the variable stands alone, making it easy to see its value.
Equation Simplification
Simplification makes an equation easier to understand and solve. It involves reducing an equation to its simplest form by performing basic arithmetic operations.
In our given exercise, the equation \(6 = 1 \cdot n\) can be simplified by understanding that any number multiplied by 1 remains unchanged. Therefore, instead of writing "\(1 \cdot n\)", we can directly write \(n\). The simplified equation is \(n = 6\).
This process might also include:
  • Combining like terms to reduce the complexity of the equation.
  • Eliminating parentheses by performing the operations contained within them.
  • Reducing fractions or factoring expressions.
Simplifying equations not only makes them easier to solve but also helps prevent errors, as fewer operations mean fewer opportunities to make a mistake.

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

The application problems that follow may involve more than merely division. Some may require addition, subtraction, or multiplication, whereas others may use a combination of two or more operations. Fitness Walking The guidelines for fitness now indicate that a person who walks \(10,000\) steps daily is physically fit. According to The Walking Site on the Internet, it takes just over \(2,000\) steps to walk one mile. If that is the case, how many miles do you need to walk in order to take \(10,000\) steps? (image cannot copy)

Add each of the following. (All problems involve carrying in at least one column. $$\begin{array}{r} 682 \\ 193 \\ \hline \end{array}$$

The application problems that follow may involve more than merely division. Some may require addition, subtraction, or multiplication, whereas others may use a combination of two or more operations. Filling Glasses How many 5 -ounce glasses can be filled from a 32 -ounce bottle of milk? How many ounces of milk will be left in the bottle when all the glasses are full?

Add each of the following. (All problems involve carrying in at least one column. $$\begin{array}{r} 5,637 \\ 481 \\ 7,899 \\ \hline \end{array}$$

Filling Glasses How many 5 -ounce glasses can be filled from a 32 -ounce bottle of milk? How many ounces of milk will be left in the bottle when all the glasses are full?Filling Glasses How many 3 -ounce glasses can be filled from a 28 - ounce bottle of milk? How many ounces of milk will be left in the bottle when all the glasses are filled?
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

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.