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,...
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![**Solve the Equation**
Given the equation:
\[
\frac{2}{5}(w - 12) = -25
\]
**Steps to Solve:**
1. **Distribute the Fraction:**
Multiply both sides of the equation by 5 to eliminate the fraction:
\[
2(w - 12) = -125
\]
2. **Simplify the Equation:**
Distribute the 2 on the left side:
\[
2w - 24 = -125
\]
3. **Isolate the Variable \( w \):**
Add 24 to both sides to solve for \( w \):
\[
2w = -101
\]
4. **Solve for \( w:**
Divide both sides by 2:
\[
w = -50.5
\]
**Solution:**
The value of \( w \) is \(-50.5\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe927df63-f1e3-498b-a31a-923bb5077d27%2F1b24cf50-00b4-4816-b4fc-89161c7aa15d%2F1ivvox.jpeg&w=3840&q=75)
Transcribed Image Text:**Solve the Equation**
Given the equation:
\[
\frac{2}{5}(w - 12) = -25
\]
**Steps to Solve:**
1. **Distribute the Fraction:**
Multiply both sides of the equation by 5 to eliminate the fraction:
\[
2(w - 12) = -125
\]
2. **Simplify the Equation:**
Distribute the 2 on the left side:
\[
2w - 24 = -125
\]
3. **Isolate the Variable \( w \):**
Add 24 to both sides to solve for \( w \):
\[
2w = -101
\]
4. **Solve for \( w:**
Divide both sides by 2:
\[
w = -50.5
\]
**Solution:**
The value of \( w \) is \(-50.5\).
![Certainly! Here is the transcription of the handwritten notes, suitable for an educational website:
---
### Problem Solving Example:
1. Start with the equation:
\[
\frac{2}{5} (W - 12) - 25 = \frac{x}{\frac{3}{2}}
\]
2. Work through the solution:
- Multiply both sides by \(\frac{5}{2}\) to eliminate the fraction:
\[
W - 12 = -62.5
\]
- Add 12 to both sides to solve for \(W\):
\[
W = -62.5 + 12 = -50.5
\]
### Explanation:
- **Equation Breakdown**: The original equation is a linear equation with fractions. Solving it involves isolating the variable \(W\) by performing operations on both sides of the equation.
- **Steps**:
- Eliminate the fraction by multiplying by the reciprocal.
- Simplify the equation by combining and isolating terms.
### Conclusion:
The solution to the equation is \(W = -50.5\).
---
This transcription explains each step in detail and provides a structured approach to solving linear equations with fractions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe927df63-f1e3-498b-a31a-923bb5077d27%2F1b24cf50-00b4-4816-b4fc-89161c7aa15d%2F33lkw5c.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Here is the transcription of the handwritten notes, suitable for an educational website:
---
### Problem Solving Example:
1. Start with the equation:
\[
\frac{2}{5} (W - 12) - 25 = \frac{x}{\frac{3}{2}}
\]
2. Work through the solution:
- Multiply both sides by \(\frac{5}{2}\) to eliminate the fraction:
\[
W - 12 = -62.5
\]
- Add 12 to both sides to solve for \(W\):
\[
W = -62.5 + 12 = -50.5
\]
### Explanation:
- **Equation Breakdown**: The original equation is a linear equation with fractions. Solving it involves isolating the variable \(W\) by performing operations on both sides of the equation.
- **Steps**:
- Eliminate the fraction by multiplying by the reciprocal.
- Simplify the equation by combining and isolating terms.
### Conclusion:
The solution to the equation is \(W = -50.5\).
---
This transcription explains each step in detail and provides a structured approach to solving linear equations with fractions.
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