Intermediate Algebra
Intermediate Algebra
19th Edition
ISBN: 9780998625720
Author: Lynn Marecek
Publisher: OpenStax College
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### Problem 34: Inequality Solution Using the One-Point Test **Objective:** Solve the inequality \(6x + 5y > 20\) using the one-point test and visualize the solution by shading the appropriate region. **Steps:** 1. **Graph the Boundary Line:** - The inequality \(6x + 5y > 20\) will have a boundary line \(6x + 5y = 20\). - Convert to slope-intercept form for easier graphing: - \(5y = -6x + 20\) - \(y = -\frac{6}{5}x + 4\) 2. **Determine One-Point Test:** - Choose a test point not on the line, typically \( (0, 0) \) if it is not on the line. - Substitute \(x = 0\) and \(y = 0\) into the inequality: - \(6(0) + 5(0) > 20\) - \(0 > 20\) (False) - Since the point \((0, 0)\) does not satisfy the inequality, shade the region on the opposite side of the line. 3. **Shade the Solution:** - Shade the area where the inequality \(6x + 5y > 20\) holds true, which is the region that does not include the point \((0, 0)\). By summarizing these steps, students will solve the inequality and shade the appropriate region to visualize the solution on a graph.
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Transcribed Image Text:### Problem 34: Inequality Solution Using the One-Point Test **Objective:** Solve the inequality \(6x + 5y > 20\) using the one-point test and visualize the solution by shading the appropriate region. **Steps:** 1. **Graph the Boundary Line:** - The inequality \(6x + 5y > 20\) will have a boundary line \(6x + 5y = 20\). - Convert to slope-intercept form for easier graphing: - \(5y = -6x + 20\) - \(y = -\frac{6}{5}x + 4\) 2. **Determine One-Point Test:** - Choose a test point not on the line, typically \( (0, 0) \) if it is not on the line. - Substitute \(x = 0\) and \(y = 0\) into the inequality: - \(6(0) + 5(0) > 20\) - \(0 > 20\) (False) - Since the point \((0, 0)\) does not satisfy the inequality, shade the region on the opposite side of the line. 3. **Shade the Solution:** - Shade the area where the inequality \(6x + 5y > 20\) holds true, which is the region that does not include the point \((0, 0)\). By summarizing these steps, students will solve the inequality and shade the appropriate region to visualize the solution on a graph.
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