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6) Use the graph to solve the equation and inequalities. (a) 4x 2 = -3x +5 (b) 4x- 2 < -3x + 5 (c) 4x-2 2-3x + 5 21

6) Use the graph to solve the equation and inequalities. (a) 4x 2 = -3x +5 (b) 4x- 2 < -3x + 5 (c) 4x-2 2-3x + 5 21

Algebra and Trigonometry (6th Edition)
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 Equations and Inequalities Using Graphs:** **Question 6:** Use the graph to solve the equation and inequalities. (a) \( 4x - 2 = -3x + 5 \) (b) \( 4x - 2 < -3x + 5 \) (c) \( 4x - 2 \geq -3x + 5 \) **Explanation:** The given graph illustrates two linear equations: 1. \( y_1 = 4x - 2 \) (plotted in blue) 2. \( y_2 = -3x + 5 \) (plotted in pink) The point of intersection between the two lines is marked on the graph and labeled as \((1, 2)\). - For part (a), the solution to \( 4x - 2 = -3x + 5 \) is the x-coordinate of the intersection point, which is \( x = 1 \). - For part (b), determine the range of \( x \) values where the blue line \( y_1 = 4x - 2 \) is below the pink line \( y_2 = -3x + 5 \). The inequality \( 4x - 2 < -3x + 5 \) holds for \( x < 1 \). - For part (c), determine the range of \( x \) values where the blue line \( y_1 = 4x - 2 \) is on or above the pink line \( y_2 = -3x + 5 \). The inequality \( 4x - 2 \geq -3x + 5 \) holds for \( x \geq 1 \). Thus, the graph visually demonstrates the solution to the equation and inequalities by representing the relationships between the lines.
Transcribed Image Text:**Solving Equations and Inequalities Using Graphs:** **Question 6:** Use the graph to solve the equation and inequalities. (a) \( 4x - 2 = -3x + 5 \) (b) \( 4x - 2 < -3x + 5 \) (c) \( 4x - 2 \geq -3x + 5 \) **Explanation:** The given graph illustrates two linear equations: 1. \( y_1 = 4x - 2 \) (plotted in blue) 2. \( y_2 = -3x + 5 \) (plotted in pink) The point of intersection between the two lines is marked on the graph and labeled as \((1, 2)\). - For part (a), the solution to \( 4x - 2 = -3x + 5 \) is the x-coordinate of the intersection point, which is \( x = 1 \). - For part (b), determine the range of \( x \) values where the blue line \( y_1 = 4x - 2 \) is below the pink line \( y_2 = -3x + 5 \). The inequality \( 4x - 2 < -3x + 5 \) holds for \( x < 1 \). - For part (c), determine the range of \( x \) values where the blue line \( y_1 = 4x - 2 \) is on or above the pink line \( y_2 = -3x + 5 \). The inequality \( 4x - 2 \geq -3x + 5 \) holds for \( x \geq 1 \). Thus, the graph visually demonstrates the solution to the equation and inequalities by representing the relationships between the lines.
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