Problem 54 Solve using the addition princip... [FREE SOLUTION]

Chapter 2: Problem 54

Solve using the addition principle. $$ -8 n+12>12-7 n $$

Short Answer

Expert verified

n < 0

Step by step solution

Isolate the variable term

Move the variable terms on one side of the inequality by adding or subtracting the same term from both sides. Here, we will add $-7n$ to both sides: $-8n + 12 + 7n > 12 - 7n + 7n$This simplifies to: $-n + 12 > 12$

Move constant term

Next, subtract 12 from both sides to isolate the variable term \-n\ on the left side: $-n + 12 - 12 > 12 - 12$Which simplifies to: $-n > 0$

Solve for n

Divide both sides by -1 and reverse the inequality sign to solve for \: $\frac{-n}{-1} < \frac{0}{-1}$This simplifies to: $n < 0$

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.

Addition Principle

The addition principle is a crucial concept in solving inequalities and equations. It states that you can add the same number to both sides of an inequality or equation without changing the inequality's direction. This helps in moving terms around to isolate the variable. For example, in the given problem $-8n + 12 > 12 - 7n$, we add $-7n$ to both sides to group all variable terms on one side. This process doesn't affect the inequality but simplifies it. Remember, the same principle applies if you are subtracting a term since subtraction is just adding a negative.

Isolation of Variable

In solving inequalities, the goal is to get the variable by itself on one side of the inequality sign. This process is known as 'isolation of variable'. Let's take the problem $-8n + 12 > 12 - 7n$: first, we used the addition principle to combine like terms. Now we have $-n + 12 > 12$. The next step is to move the constant term (12) from the left side to the right side by subtracting 12 from both sides. When we do this, we get $-n > 0$, further isolating our variable term. Through these steps, we've systematically worked to isolate 'n' so it can be easily solved.

Inequality Solving Steps

Solving inequalities involves a series of specific steps. Here's a simple breakdown:

Step 1: Use the addition principle to move all variable terms to one side.
Step 2: Isolate the variable term by moving constant terms to the opposite side.
Step 3: Solve for the variable. When dividing or multiplying by a negative number, remember to reverse the inequality sign.

In our problem, we initially added $-7n$ to both sides, then subtracted 12, and finally divided by \-1\, remembering to reverse the inequality. This method ensures we maintain the inequality's integrity while isolating and solving for the variable.

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 using the addition principle. $$ -8 n+12>12-7 n $$

Short Answer

Step by step solution

Isolate the variable term

Move constant term

Solve for n

Key Concepts

Addition Principle

Isolation of Variable

Inequality Solving Steps

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Statistics

Logic and Functions

Theoretical and Mathematical Physics

Calculus

Probability and Statistics

Study anywhere. Anytime. Across all devices.