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What is the solution to the inequality |2x + 3 < 7? 04 10 Ox<-5 or x > 2

What is the solution to the inequality |2x + 3 < 7? 04 10 Ox<-5 or x > 2

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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What is the solution to the inequality |2x + 3| < 7 ? 4 < x < 10; - 5 < x < 2 x < 4 or x > 10; x < - 5 or x > 2
### Solving Inequalities with Absolute Values **Question:** What is the solution to the inequality |2x + 3| < 7? **Options:** 1. ○ 4 < x < 10 2. ○ -5 < x < 2 3. ○ x < 4 or x > 10 4. ○ x < -5 or x > 2 ### Explanation: To solve the absolute value inequality |2x + 3| < 7, we follow these steps: 1. Recall that for any absolute value inequality |A| < B, the inequality can be split into -B < A < B. 2. Applying this to the inequality |2x + 3| < 7, we get: -7 < 2x + 3 < 7 3. Now, solve the compound inequality by separating it into two parts: -7 < 2x + 3 AND 2x + 3 < 7 4. Isolate x in both inequalities: - Subtract 3 from all parts of the first inequality: -7 - 3 < 2x -10 < 2x (Divide by 2) -5 < x - Subtract 3 from all parts of the second inequality: 2x + 3 - 3 < 7 - 3 2x < 4 (Divide by 2) x < 2 5. Combining both parts we get: -5 < x < 2 This is the solution to the inequality. Therefore, the correct answer is: ○ -5 < x < 2
Transcribed Image Text:### Solving Inequalities with Absolute Values **Question:** What is the solution to the inequality |2x + 3| < 7? **Options:** 1. ○ 4 < x < 10 2. ○ -5 < x < 2 3. ○ x < 4 or x > 10 4. ○ x < -5 or x > 2 ### Explanation: To solve the absolute value inequality |2x + 3| < 7, we follow these steps: 1. Recall that for any absolute value inequality |A| < B, the inequality can be split into -B < A < B. 2. Applying this to the inequality |2x + 3| < 7, we get: -7 < 2x + 3 < 7 3. Now, solve the compound inequality by separating it into two parts: -7 < 2x + 3 AND 2x + 3 < 7 4. Isolate x in both inequalities: - Subtract 3 from all parts of the first inequality: -7 - 3 < 2x -10 < 2x (Divide by 2) -5 < x - Subtract 3 from all parts of the second inequality: 2x + 3 - 3 < 7 - 3 2x < 4 (Divide by 2) x < 2 5. Combining both parts we get: -5 < x < 2 This is the solution to the inequality. Therefore, the correct answer is: ○ -5 < x < 2
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