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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![### Educational Content Transcription
**Equation:**
\[ \text{b. } -31 = \frac{3}{5}x - 10 \]
**Instructions:**
- This problem is an example of a linear equation involving fractions.
- To solve for \( x \), isolate the variable on one side.
**Steps to Solve:**
1. **Add 10 to both sides of the equation** to balance the equation:
\[ -31 + 10 = \frac{3}{5}x - 10 + 10 \]
\[ -21 = \frac{3}{5}x \]
2. **Multiply both sides of the equation by the reciprocal of \(\frac{3}{5}\)** to solve for \( x \):
\[ -21 \times \frac{5}{3} = x \]
\[ x = -35 \]
**Check the Solution:**
- Substitute \( x = -35 \) back into the original equation to verify:
\[ -31 \stackrel{?}{=} \frac{3}{5}(-35) - 10 \]
\[ -31 \stackrel{?}{=} -21 - 10 \]
\[ -31 = -31 \] (True)
Thus, the solution \( x = -35 \) is correct.
**Additional Elements in the Image:**
- **Pen:** A blue pen is placed on top of the paper, labeled "Pentel EnerGel 0.7MM BL27."
- **Paper texture**: The edge of a textured paper, possibly a napkin or paper towel, with a patterned design is visible at the bottom of the image.
- **Background text:** There is faint and partially visible text in the background, not relevant to the current mathematical problem.
This equation-solving example helps illustrate the process of dealing with linear equations involving fractions for educational purposes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F406d348b-fbb7-4bba-911a-31fffdc94d1a%2Fbffe6229-b015-4235-b1aa-fedb2e02d070%2F2zfuj3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Content Transcription
**Equation:**
\[ \text{b. } -31 = \frac{3}{5}x - 10 \]
**Instructions:**
- This problem is an example of a linear equation involving fractions.
- To solve for \( x \), isolate the variable on one side.
**Steps to Solve:**
1. **Add 10 to both sides of the equation** to balance the equation:
\[ -31 + 10 = \frac{3}{5}x - 10 + 10 \]
\[ -21 = \frac{3}{5}x \]
2. **Multiply both sides of the equation by the reciprocal of \(\frac{3}{5}\)** to solve for \( x \):
\[ -21 \times \frac{5}{3} = x \]
\[ x = -35 \]
**Check the Solution:**
- Substitute \( x = -35 \) back into the original equation to verify:
\[ -31 \stackrel{?}{=} \frac{3}{5}(-35) - 10 \]
\[ -31 \stackrel{?}{=} -21 - 10 \]
\[ -31 = -31 \] (True)
Thus, the solution \( x = -35 \) is correct.
**Additional Elements in the Image:**
- **Pen:** A blue pen is placed on top of the paper, labeled "Pentel EnerGel 0.7MM BL27."
- **Paper texture**: The edge of a textured paper, possibly a napkin or paper towel, with a patterned design is visible at the bottom of the image.
- **Background text:** There is faint and partially visible text in the background, not relevant to the current mathematical problem.
This equation-solving example helps illustrate the process of dealing with linear equations involving fractions for educational purposes.
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