Problem 10 Solve. Don't forget to check! ... [FREE SOLUTION]

91影视

Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 11: Problem 10

Solve. Don't forget to check! $$ 5 x+4=-41 $$

Short Answer

Expert verified

x = -9

Step by step solution

- Isolate the variable term

The equation given is 5x + 4 = -41. To isolate the term with the variable, subtract 4 from both sides of the equation. This gives: 5x + 4 - 4 = -41 - 4, hence 5x = -45.

- Solve for the variable

Now, solve for x by dividing both sides of the equation by 5. Therefore, $ x = \frac{-45}{5} $, which simplifies to $ x = -9 $.

- Check the solution

Substitute x = -9 back into the original equation to verify the solution: 5(-9) + 4 should equal -41. Calculating this, -45 + 4 = -41, confirming that 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

To solve a linear equation like the given example, our first goal is to isolate the term that contains the variable. This typically means removing any constants from the variable term.
In the equation 5x + 4 = -41, we need to get rid of the +4 on the left side to isolate the variable term, which is 5x.
We can do this by performing the inverse operation of addition, which is subtraction.
So, we subtract 4 from both sides of the equation:
5x + 4 - 4 = -41 - 4
This simplifies to 5x = -45.
Congratulations! We have successfully isolated the variable term on one side of the equation.

Solve for the Variable

Now that we have 5x = -45, the next step is to solve for the variable x. This means we need to get x by itself on one side of the equation.
Since 5x means 5 times x, we can undo this multiplication by dividing both sides of the equation by 5.
So, we divide both sides by 5:
$ x = \frac{-45}{5} $
This simplifies to:
$ x = -9 $
Now we have our solution, x = -9!
This step ensures that we pinpoint the exact value of the variable that satisfies the equation.

Check the Solution

After we've found x = -9, it's crucial to check our solution to confirm it's correct. This step helps verify that we didn't make any errors in our calculations.
We do this by substituting x = -9 back into the original equation and seeing if it holds true:
The original equation is 5x + 4 = -41.
Substitute x = -9:
5(-9) + 4 = -41
Now, calculate the left side:
-45 + 4 = -41
Since both sides of the equation are equal (-41 = -41), our solution is verified as correct.
This final check confirms the accuracy of our work and reinforces our understanding of the process.

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. Don't forget to check! $$ 5 x+4=-41 $$

Short Answer

Step by step solution

- Isolate the variable term

- Solve for the variable

- Check the solution

Key Concepts

Isolate the Variable

Solve for the Variable

Check the Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Pure Maths

Theoretical and Mathematical Physics

Geometry

Logic and Functions

Probability and Statistics

Study anywhere. Anytime. Across all devices.