W. Graph the solution set: x-2y≤-2 x+120 V₁ of y

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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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.
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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