Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
Solve equation and write out the check
![### Solve the equation. Write out the check.
\[
\frac{p}{3} - \frac{3p}{8} = 3
\]
#### Show your work here:
* (This section should be used to detail the steps taken to solve the equation. Start by finding a common denominator to combine the fractions.)
#### Write your solution here:
* (This section should be used to write out the final value of \( p \) after solving the equation.)
#### Write out your check here:
* (This section should be used to substitute the value of \( p \) back into the original equation to verify that it is correct.)
### Steps to Solve the Equation:
1. Start with the given equation:
\[
\frac{p}{3} - \frac{3p}{8} = 3
\]
2. Find the common denominator for the fractions which is 24:
\[
\left(\frac{p}{3} \times \frac{8}{8}\right) - \left(\frac{3p}{8} \times \frac{3}{3}\right) = 3
\]
Simplifying the left side, we get:
\[
\frac{8p}{24} - \frac{9p}{24} = 3
\]
3. Combine the fractions:
\[
\frac{8p - 9p}{24} = 3
\]
This simplifies to:
\[
\frac{-p}{24} = 3
\]
4. Solve for \( p \):
Multiply both sides by \(-24\) to isolate \( p \):
\[
p = -72
\]
#### Write your solution here:
\(
p = -72
\)
#### Write out your check here:
Substitute \( p = -72 \) in the original equation to verify:
\[
\frac{-72}{3} - \frac{3 \times (-72)}{8} = 3
\]
Simplifying each term:
\[
-24 + 27 = 3
\]
Which simplifies to:
\[
3 = 3
\]
The left side of the equation equals the right side; thus, the solution \( p = -72 \) is correct.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29666072-4841-4557-93a0-541aeee2aafd%2F9bf94b3e-e0c7-403d-8f1c-40103911c6b0%2Fsyggzbm_processed.png&w=3840&q=75)
Transcribed Image Text:### Solve the equation. Write out the check.
\[
\frac{p}{3} - \frac{3p}{8} = 3
\]
#### Show your work here:
* (This section should be used to detail the steps taken to solve the equation. Start by finding a common denominator to combine the fractions.)
#### Write your solution here:
* (This section should be used to write out the final value of \( p \) after solving the equation.)
#### Write out your check here:
* (This section should be used to substitute the value of \( p \) back into the original equation to verify that it is correct.)
### Steps to Solve the Equation:
1. Start with the given equation:
\[
\frac{p}{3} - \frac{3p}{8} = 3
\]
2. Find the common denominator for the fractions which is 24:
\[
\left(\frac{p}{3} \times \frac{8}{8}\right) - \left(\frac{3p}{8} \times \frac{3}{3}\right) = 3
\]
Simplifying the left side, we get:
\[
\frac{8p}{24} - \frac{9p}{24} = 3
\]
3. Combine the fractions:
\[
\frac{8p - 9p}{24} = 3
\]
This simplifies to:
\[
\frac{-p}{24} = 3
\]
4. Solve for \( p \):
Multiply both sides by \(-24\) to isolate \( p \):
\[
p = -72
\]
#### Write your solution here:
\(
p = -72
\)
#### Write out your check here:
Substitute \( p = -72 \) in the original equation to verify:
\[
\frac{-72}{3} - \frac{3 \times (-72)}{8} = 3
\]
Simplifying each term:
\[
-24 + 27 = 3
\]
Which simplifies to:
\[
3 = 3
\]
The left side of the equation equals the right side; thus, the solution \( p = -72 \) is correct.
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