Problem 33 Solve equation, and check your s... [FREE SOLUTION]

91影视

Chapter 2: Problem 33

Solve equation, and check your solution. \(4 r=0\)

Short Answer

Expert verified

The solution is \(r = 0\).

Step by step solution

Identify the Equation

The given equation is: \(4r = 0\)

Isolate the Variable

To isolate the variable \(r\), divide both sides of the equation by 4: \(\frac{4r}{4} = \frac{0}{4}\)

Simplify

Simplify both sides of the equation: \(r = 0\)

Check the Solution

Substitute \(r = 0\) back into the original equation to verify: \(4r = 4(0) = 0\). The original equation holds true, thus the solution is correct.

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.

Isolate the Variable

The first step in solving linear equations is to isolate the variable. This means getting the variable by itself on one side of the equation. For our exercise, we start with the equation:
\(4r = 0\)
To isolate \(r\), we need to remove the coefficient that is multiplying \(r\). In this case, the coefficient is 4. We do this by performing the opposite operation, which is division. Here鈥檚 how:

Divide both sides of the equation by 4: \(\frac{4r}{4} = \frac{0}{4}\)
This simplifies to: \(r = 0\).

Now, \(r\) is isolated and our equation is simpler to work with. This fundamental step is crucial as it sets the stage for solving the equation.

Simplify Equations

Next, we need to simplify the equation. Simplification involves reducing an equation to its simplest form. After isolating the variable \(r\) in the equation:
\(4r = 0\),
we divided by 4 and found:
\(r = 0\).
This step essentially involves performing basic arithmetic operations to make the equation as straightforward as possible. It ensures that the variable is on its own and the other side of the equation is simplified:

On one side of the equation, we have \(r\).
On the other side, we have a number, in this case, 0.

Simplifying helps to clearly see the solution, reducing the chances of errors and misinterpretations. Always aim for the simplest form of the equation!

Check the Solution

The final step is checking the solution. Verifying your solution is crucial to ensure the accuracy of your work. Here's how you can check your answer from the exercise:
You found that \(r = 0\). To confirm this, substitute \(r\) back into the original equation:
\(4r = 0\)
Replace \(r\) with 0:
\( 4(0) = 0\)
Since the left side equals the right side (\(0 = 0\)), the solution \(r = 0\) is correct.

Substitution helps verify that your answer satisfies the original equation.
It provides a double-check against any mistakes made during calculation.

Always double-check your solutions to confirm their correctness before finalizing your answer. This practice will build confidence and accuracy in solving equations.

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 equation, and check your solution. \(4 r=0\)

Short Answer

Step by step solution

Identify the Equation

Isolate the Variable

Simplify

Check the Solution

Key Concepts

Isolate the Variable

Simplify Equations

Check the Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Calculus

Pure Maths

Theoretical and Mathematical Physics

Probability and Statistics

Study anywhere. Anytime. Across all devices.