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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![### Solving Inequalities
#### Question:
What is the solution of this inequality?
\[ 1.6 \geq 0.8x + 4 \]
#### Options:
- (a) \( 7 \leq x \)
- (b) \( 7 \geq x \)
- (c) \( -3 \leq x \)
- (d) \( -3 \geq x \)
##### Solution:
First, let's solve the inequality step-by-step:
1. **Start with the given inequality:**
\[ 1.6 \geq 0.8x + 4 \]
2. **Isolate the variable term:**
Subtract 4 from both sides:
\[ 1.6 - 4 \geq 0.8x \]
Simplify the left side:
\[ -2.4 \geq 0.8x \]
3. **Solve for \( x \):**
Divide both sides by 0.8:
\[ \frac{-2.4}{0.8} \geq x \]
\[ -3 \geq x \]
Or equivalently:
\[ x \leq -3 \]
Thus, the solution is:
- \( x \leq -3 \)
#### Answer:
- (d) \( -3 \geq x \)
In this case, option (d) represents the correct answer as it implies the same as \( x \leq -3 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6623ba39-4d5f-4211-9936-230d4bb3a04c%2F30fc112d-3d77-4d80-a796-37484a193e20%2F2sgl43g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving Inequalities
#### Question:
What is the solution of this inequality?
\[ 1.6 \geq 0.8x + 4 \]
#### Options:
- (a) \( 7 \leq x \)
- (b) \( 7 \geq x \)
- (c) \( -3 \leq x \)
- (d) \( -3 \geq x \)
##### Solution:
First, let's solve the inequality step-by-step:
1. **Start with the given inequality:**
\[ 1.6 \geq 0.8x + 4 \]
2. **Isolate the variable term:**
Subtract 4 from both sides:
\[ 1.6 - 4 \geq 0.8x \]
Simplify the left side:
\[ -2.4 \geq 0.8x \]
3. **Solve for \( x \):**
Divide both sides by 0.8:
\[ \frac{-2.4}{0.8} \geq x \]
\[ -3 \geq x \]
Or equivalently:
\[ x \leq -3 \]
Thus, the solution is:
- \( x \leq -3 \)
#### Answer:
- (d) \( -3 \geq x \)
In this case, option (d) represents the correct answer as it implies the same as \( x \leq -3 \).
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