Problem 31 Solve. See Examples 2 through 8.... [FREE SOLUTION]

91影视

Chapter 2: Problem 31

Solve. See Examples 2 through 8. $$ n-5=-55 $$

Short Answer

Expert verified

The solution is $ n = -50 $.

Step by step solution

Identify the Equation

The original equation given to solve is $ n - 5 = -55 $. This is a simple linear equation.

Isolate the Variable

To find the value of $ n $, we need to isolate it on one side of the equation. We can do this by adding 5 to both sides. The equation changes as follows: $ n - 5 + 5 = -55 + 5 $.

Simplify both Sides

On the left side, $-5 + 5$ simplifies to 0, leaving $ n $. On the right side, $-55 + 5$ simplifies to $-50$. So the simplified equation is $ n = -50 $.

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

Solving equations involves finding the value of unknown variables in mathematical statements. When working with linear equations, these are typically in the form of a simple algebraic expression with a single variable.

In our exercise, the equation was given as $ n - 5 = -55 $. The goal is to determine the value of $ n $ that makes this equation true. Solving equations often requires a few strategic steps:

Understanding the structure: Recognize that the equation involves an operation that needs to be reversed or altered to solve for the variable.
Performing operations on both sides: This maintains the equation's balance since whatever operation you perform on one side, you must also do on the other.

To solve effectively, you must adhere carefully to these fundamental procedures, ensuring both sides remain equal throughout the solving process.

Isolation of Variables

Isolation of variables is a critical step in solving equations. It is the process of rearranging the equation to get the unknown variable on its own on one side of the equation. Doing this helps in identifying the exact value of the variable.

In the example $ n - 5 = -55 $, the variable $ n $ is not isolated. To isolate $ n $:

Add 5 to both sides of the equation, which works counter to the subtraction in the equation. This is because adding and subtracting are inverse operations.

The result is an equation where $ n $ is on its own: $ n = -55 + 5 $. Here, adding 5 cancels out the $-5$ on the left side, effectively isolating $ n $. This key step simplifies the process, making solving for the variable much more direct.

Equation Simplification

Equation simplification is the process of making an equation easier to understand and solve. It involves performing arithmetic operations so that one side of the equation results in a single variable, and the other side gives its corresponding constant value.

In step 3 of the solution for $ n - 5 = -55 $, after adding 5 to both sides, the left side simplifies to $ n $ because $-5 + 5 = 0$. The process follows as:

The left side converts from $ n - 5 + 5 $ to simply $ n $.
On the right side, the operation $-55 + 5$ simplifies to $-50$.

Thus, the equation simplifies to $ n = -50 $, providing a clear and final solution. Simplifying equations is crucial as it helps in directly seeing the results without unnecessary complexities.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Solve. See Examples 2 through 8. $$ n-5=-55 $$

Short Answer

Step by step solution

Identify the Equation

Isolate the Variable

Simplify both Sides

Key Concepts

Solving Equations

Isolation of Variables

Equation Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Applied Mathematics

Calculus

Theoretical and Mathematical Physics

Probability and Statistics

Study anywhere. Anytime. Across all devices.