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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![**Select each solution to the inequality below.**
\(\frac{1}{2}(x - 8) < 2\)
- [ ] -12
- [ ] -4
- [ ] 18
- [x] 12
- [ ] 0
**Explanation:**
To solve the inequality:
1. Distribute the \(\frac{1}{2}\) across the expression:
\[
\frac{1}{2} \cdot (x - 8) = \frac{1}{2}x - 4
\]
2. Set up the inequality:
\[
\frac{1}{2}x - 4 < 2
\]
3. Add 4 to both sides to isolate the \(\frac{1}{2}x\):
\[
\frac{1}{2}x < 6
\]
4. Multiply both sides by 2 to solve for \(x\):
\[
x < 12
\]
The solution to the inequality is all \(x\) values less than 12. From the options provided, 12 is a potential candidate. However, since \(x\) must be strictly less than 12, none of the provided values satisfy the inequality because 12 is not less than 12. Only values actually less than 12 would satisfy original inequality.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb21401a3-a258-4868-b8b5-14a864017c10%2Fcc2b0503-b1ec-474c-a1cd-4f3eeb2190ed%2Fxv0q1nq_processed.png&w=3840&q=75)
Transcribed Image Text:**Select each solution to the inequality below.**
\(\frac{1}{2}(x - 8) < 2\)
- [ ] -12
- [ ] -4
- [ ] 18
- [x] 12
- [ ] 0
**Explanation:**
To solve the inequality:
1. Distribute the \(\frac{1}{2}\) across the expression:
\[
\frac{1}{2} \cdot (x - 8) = \frac{1}{2}x - 4
\]
2. Set up the inequality:
\[
\frac{1}{2}x - 4 < 2
\]
3. Add 4 to both sides to isolate the \(\frac{1}{2}x\):
\[
\frac{1}{2}x < 6
\]
4. Multiply both sides by 2 to solve for \(x\):
\[
x < 12
\]
The solution to the inequality is all \(x\) values less than 12. From the options provided, 12 is a potential candidate. However, since \(x\) must be strictly less than 12, none of the provided values satisfy the inequality because 12 is not less than 12. Only values actually less than 12 would satisfy original inequality.
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