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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![**Title: Solving Inequalities - Graph Representation**
**Question:**
*Which graph best represents the solution to \( \frac{7}{8} \geq \frac{1}{4} x + \frac{1}{2} \)?*
**Explanation:**
Consider the given inequality:
\[ \frac{7}{8} \geq \frac{1}{4} x + \frac{1}{2} \]
First, to solve this inequality, isolate the variable \( x \):
1. Subtract \( \frac{1}{2} \) from both sides:
\[ \frac{7}{8} - \frac{1}{2} \geq \frac{1}{4} x \]
\[ \frac{7}{8} - \frac{4}{8} \geq \frac{1}{4} x \]
\[ \frac{3}{8} \geq \frac{1}{4} x \]
2. Multiply both sides by 4 to solve for \( x \):
\[ 4 \times \frac{3}{8} \geq x \]
\[ \frac{12}{8} \geq x \]
\[ \frac{3}{2} \geq x \]
\[ x \leq \frac{3}{2} \]
The inequality simplifies to \( x \leq \frac{3}{2} \).
Graphically, this means that \( x \) includes all values less than or equal to \( \frac{3}{2} \).
**Graph Description:**
The task has four options, each representing a number line graph. Let's analyze each option to determine which one correctly represents the inequality \( x \leq \frac{3}{2} \):
1. **First Graph:**
- The number line has values marked from 0 to 6.
- The section from 0 to 6 is shaded.
- This graph does not satisfy \( x \leq \frac{3}{2} \).
2. **Second Graph:**
- The number line has values marked from 0 to 6.
- The section from 0 to 1.5 is shaded, including 1.5.
- This graph correctly represents \( x \leq \frac{3}{2} \).
3. **Third Graph:**
- The number line has values](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70ccebb5-1183-4ab6-bf93-b7ae69e62bf9%2F05ed653d-13aa-48e3-bb4e-29eca30498c3%2F9yvyq2s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Solving Inequalities - Graph Representation**
**Question:**
*Which graph best represents the solution to \( \frac{7}{8} \geq \frac{1}{4} x + \frac{1}{2} \)?*
**Explanation:**
Consider the given inequality:
\[ \frac{7}{8} \geq \frac{1}{4} x + \frac{1}{2} \]
First, to solve this inequality, isolate the variable \( x \):
1. Subtract \( \frac{1}{2} \) from both sides:
\[ \frac{7}{8} - \frac{1}{2} \geq \frac{1}{4} x \]
\[ \frac{7}{8} - \frac{4}{8} \geq \frac{1}{4} x \]
\[ \frac{3}{8} \geq \frac{1}{4} x \]
2. Multiply both sides by 4 to solve for \( x \):
\[ 4 \times \frac{3}{8} \geq x \]
\[ \frac{12}{8} \geq x \]
\[ \frac{3}{2} \geq x \]
\[ x \leq \frac{3}{2} \]
The inequality simplifies to \( x \leq \frac{3}{2} \).
Graphically, this means that \( x \) includes all values less than or equal to \( \frac{3}{2} \).
**Graph Description:**
The task has four options, each representing a number line graph. Let's analyze each option to determine which one correctly represents the inequality \( x \leq \frac{3}{2} \):
1. **First Graph:**
- The number line has values marked from 0 to 6.
- The section from 0 to 6 is shaded.
- This graph does not satisfy \( x \leq \frac{3}{2} \).
2. **Second Graph:**
- The number line has values marked from 0 to 6.
- The section from 0 to 1.5 is shaded, including 1.5.
- This graph correctly represents \( x \leq \frac{3}{2} \).
3. **Third Graph:**
- The number line has values
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