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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On this chapter review can you tell me if I solved this correctly?
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![**Graph the Solution Set**
This educational page provides a step-by-step guide to graphing the solution set of the linear inequality:
\[ x - 2y \leq -2 \]
**Solution Steps:**
1. **Rewrite the Inequality as an Equation:**
Start by converting the inequality into an equation to find the boundary line:
\[ x - 2y = -2 \]
2. **Solve for \( y \):**
\[
x - 2y = -2 \quad \Rightarrow \quad -2y = -x - 2
\]
\[
y = \frac{-x - 2}{-2} \quad \Rightarrow \quad y = \frac{1}{2}x + 1
\]
3. **Graph the Line:**
- The line \( y = \frac{1}{2}x + 1 \) is graphed as a solid line because the inequality is \(\leq\), indicating the boundary is part of the solution.
- The line intercepts the y-axis at \( (0, 1) \) and has a slope of \(\frac{1}{2}\).
4. **Shade the Region:**
- The inequality \( x - 2y \leq -2 \) corresponds to the region below the line. Shade the area below the line to indicate the solution set, as the inequality involves "less than or equal to."
**Additional Information:**
- There is another inequality written on the page:
\[ x + 1 \geq 0 \]
This inequality simplifies to \( x \geq -1 \), suggesting that only values where \( x \) is greater than or equal to -1 are included within the solution set.
The overall graphed solution set is the intersection of these shaded regions on the coordinate plane.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7d898221-0a5e-4da1-9d91-04a92a972c27%2Fc9e8efcf-1a77-40a1-a3e5-99421db8b980%2Fwgg2xwg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Graph the Solution Set**
This educational page provides a step-by-step guide to graphing the solution set of the linear inequality:
\[ x - 2y \leq -2 \]
**Solution Steps:**
1. **Rewrite the Inequality as an Equation:**
Start by converting the inequality into an equation to find the boundary line:
\[ x - 2y = -2 \]
2. **Solve for \( y \):**
\[
x - 2y = -2 \quad \Rightarrow \quad -2y = -x - 2
\]
\[
y = \frac{-x - 2}{-2} \quad \Rightarrow \quad y = \frac{1}{2}x + 1
\]
3. **Graph the Line:**
- The line \( y = \frac{1}{2}x + 1 \) is graphed as a solid line because the inequality is \(\leq\), indicating the boundary is part of the solution.
- The line intercepts the y-axis at \( (0, 1) \) and has a slope of \(\frac{1}{2}\).
4. **Shade the Region:**
- The inequality \( x - 2y \leq -2 \) corresponds to the region below the line. Shade the area below the line to indicate the solution set, as the inequality involves "less than or equal to."
**Additional Information:**
- There is another inequality written on the page:
\[ x + 1 \geq 0 \]
This inequality simplifies to \( x \geq -1 \), suggesting that only values where \( x \) is greater than or equal to -1 are included within the solution set.
The overall graphed solution set is the intersection of these shaded regions on the coordinate plane.
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