### Solving Rational Equations **Solve for \( x \):** \[ \frac{5x - 22}{-3} = -6 \] This problem requires you to isolate the variable \( x \). Follow these steps to solve the equation and simplify your answer: 1. Multiply both sides of the equation by \(-3\) to clear the fraction: \[ 5x - 22 = (-6) \cdot (-3) \] 2. Simplify the right side: \[ 5x - 22 = 18 \] 3. Add 22 to both sides to isolate the term with \( x \): \[ 5x = 18 + 22 \] 4. Simplify the right side: \[ 5x = 40 \] 5. Divide both sides by 5: \[ x = \frac{40}{5} \] 6. Simplify the fraction: \[ x = 8 \] **Answer:** \[ x = 8 \] Make sure you substitute \( x = 8 \) back into the original equation to verify that the solution is correct. This ensures that no mistakes were made during the solving process.
### Solving Rational Equations **Solve for \( x \):** \[ \frac{5x - 22}{-3} = -6 \] This problem requires you to isolate the variable \( x \). Follow these steps to solve the equation and simplify your answer: 1. Multiply both sides of the equation by \(-3\) to clear the fraction: \[ 5x - 22 = (-6) \cdot (-3) \] 2. Simplify the right side: \[ 5x - 22 = 18 \] 3. Add 22 to both sides to isolate the term with \( x \): \[ 5x = 18 + 22 \] 4. Simplify the right side: \[ 5x = 40 \] 5. Divide both sides by 5: \[ x = \frac{40}{5} \] 6. Simplify the fraction: \[ x = 8 \] **Answer:** \[ x = 8 \] Make sure you substitute \( x = 8 \) back into the original equation to verify that the solution is correct. This ensures that no mistakes were made during the solving process.
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
![### Solving Rational Equations
**Solve for \( x \):**
\[ \frac{5x - 22}{-3} = -6 \]
This problem requires you to isolate the variable \( x \). Follow these steps to solve the equation and simplify your answer:
1. Multiply both sides of the equation by \(-3\) to clear the fraction:
\[
5x - 22 = (-6) \cdot (-3)
\]
2. Simplify the right side:
\[
5x - 22 = 18
\]
3. Add 22 to both sides to isolate the term with \( x \):
\[
5x = 18 + 22
\]
4. Simplify the right side:
\[
5x = 40
\]
5. Divide both sides by 5:
\[
x = \frac{40}{5}
\]
6. Simplify the fraction:
\[
x = 8
\]
**Answer:**
\[ x = 8 \]
Make sure you substitute \( x = 8 \) back into the original equation to verify that the solution is correct. This ensures that no mistakes were made during the solving process.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61c70154-6dcc-4ad1-b23f-82f068f0fd01%2Fc0fcc327-072b-45b6-9a8a-9adba11c91b3%2Fo91898m.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving Rational Equations
**Solve for \( x \):**
\[ \frac{5x - 22}{-3} = -6 \]
This problem requires you to isolate the variable \( x \). Follow these steps to solve the equation and simplify your answer:
1. Multiply both sides of the equation by \(-3\) to clear the fraction:
\[
5x - 22 = (-6) \cdot (-3)
\]
2. Simplify the right side:
\[
5x - 22 = 18
\]
3. Add 22 to both sides to isolate the term with \( x \):
\[
5x = 18 + 22
\]
4. Simplify the right side:
\[
5x = 40
\]
5. Divide both sides by 5:
\[
x = \frac{40}{5}
\]
6. Simplify the fraction:
\[
x = 8
\]
**Answer:**
\[ x = 8 \]
Make sure you substitute \( x = 8 \) back into the original equation to verify that the solution is correct. This ensures that no mistakes were made during the solving process.
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