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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Question
![**Problem Statement:**
Write the following in interval notation:
\[ 2(10 - 12x) > -8 - 1x \]
**Solution Box:**
The problem requires solving the inequality and expressing the solution in interval notation. To do this, follow these steps:
1. **Expand the left side of the inequality:**
\[ 2(10 - 12x) = 20 - 24x \]
2. **Write the inequality:**
\[ 20 - 24x > -8 - 1x \]
3. **Rearrange terms to isolate \( x \):**
\[ 20 + 8 > 24x - 1x \]
\[ 28 > 23x \]
4. **Solve for \( x \):**
\[ x < \frac{28}{23} \]
5. **Express the solution in interval notation:**
\[ (-\infty, \frac{28}{23}) \]
The solution is all \( x \) values less than \( \frac{28}{23} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F99db74cb-a52b-4540-9e19-530fc4ba7537%2F55a9423c-446c-4a35-8ecc-d690568aad10%2Fhiv0w3_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Write the following in interval notation:
\[ 2(10 - 12x) > -8 - 1x \]
**Solution Box:**
The problem requires solving the inequality and expressing the solution in interval notation. To do this, follow these steps:
1. **Expand the left side of the inequality:**
\[ 2(10 - 12x) = 20 - 24x \]
2. **Write the inequality:**
\[ 20 - 24x > -8 - 1x \]
3. **Rearrange terms to isolate \( x \):**
\[ 20 + 8 > 24x - 1x \]
\[ 28 > 23x \]
4. **Solve for \( x \):**
\[ x < \frac{28}{23} \]
5. **Express the solution in interval notation:**
\[ (-\infty, \frac{28}{23}) \]
The solution is all \( x \) values less than \( \frac{28}{23} \).
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