Problem 298 In the following exercises, solv... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 8: Problem 298

In the following exercises, solve the equations with constants on both sides. $$ 32=-4-9 n $$

Short Answer

Expert verified

n = -4

Step by step solution

- Isolate the variable term

First, add 4 to both sides to move the constant to the left side of the equation: \[ 32 + 4 = -4 - 9n + 4 \]

- Simplify the equation

Combine like terms to simplify the equation: \[ 36 = -9n \]

- Solve for the variable

Divide both sides by -9 to isolate n: \[ n = \frac{36}{-9} \]

- Simplify the result

Simplify the fraction to get the final answer: \[ n = -4 \]

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.

Isolating Variables

When solving linear equations, a crucial step is isolating the variable. This means getting the variable (like in our example) by itself on one side of the equation. In our exercise, we started with the equation: 32=-4-9n.
To isolate the term with the variable (-9n), we added 4 to both sides of the equation: 32 + 4 = -4 - 9n + 4.
This brought us to the simplified equation: 36 = -9n.
Isolating the variable helps us keep track of the variable and makes it easier to solve the equation.

Combining Like Terms

Combining like terms is another essential step in solving equations. This means simplifying expressions by adding or subtracting terms that have the same variable or can be directly calculated. In our case, we combined the constants on the left side.
After adding 4 to both sides, we got: 32 + 4 = -4 + 4 - 9n.
Simplifying this, we combine the constants: 36 = -9n.
Combining like terms helps reduce the complexity of the equation and makes the next steps easier to handle.

Simplifying Algebraic Expressions

Simplifying algebraic expressions involves reducing the equation to its simplest form. Once we combined like terms, we had 36 = -9n. To isolate variable , we divided both sides by -9:36 / -9 = -9n / -9.
This gives us: n = -4.
Simplifying expressions is about performing basic arithmetic operations to make the equation as straightforward as possible.

Linear Equations with Constants

Linear equations with constants on both sides require moving constants and variable terms to separate sides. In the exercise, we had constants on both sides (32 and -4). By adding 4 to both sides, we moved the constant term from the right side to the left:32 + 4 = -4 - 9n + 4.
Then solved for the variable term by simplifying to get 36 = -9n. This approach makes it easier to isolate the variable and solve the equation.

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

In the following exercises, solve the equations with constants on both sides. $$ 32=-4-9 n $$

Short Answer

Step by step solution

- Isolate the variable term

- Simplify the equation

- Solve for the variable

- Simplify the result

Key Concepts

Isolating Variables

Combining Like Terms

Simplifying Algebraic Expressions

Linear Equations with Constants

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Applied Mathematics

Calculus

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.