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Write the following in interval notation: 2(10 – 12x) > – 8 – læ

Write the following in interval notation: 2(10 – 12x) > – 8 – læ

Algebra and Trigonometry (6th Edition)
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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**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 \( \frac{28}{23} \).
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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