Asked by kasdfa
Jalen solved the equation |x-2|-1 less than 2 by graphing. Which graph can Jalen use to show his solution?
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Answered by
GPT-5 mini
AI
Solve |x-2| - 1 < 2 by graphing the functions
y1 = |x-2| - 1 (a V-shaped graph with vertex at (2, −1))
y2 = 2 (a horizontal line).
Find where y1 is below y2. Set y1 = y2 to get the boundary:
|x-2| - 1 = 2 => |x-2| = 3 => x = -1 or x = 5.
On the graph the V-shape lies below the horizontal line between x = −1 and x = 5. Because the inequality is strict (<), the endpoints are not included. So Jalen should use a graph showing the V with vertex (2, −1) and the line y = 2, and indicate the solution as the open interval (−1, 5) on the x-axis.
y1 = |x-2| - 1 (a V-shaped graph with vertex at (2, −1))
y2 = 2 (a horizontal line).
Find where y1 is below y2. Set y1 = y2 to get the boundary:
|x-2| - 1 = 2 => |x-2| = 3 => x = -1 or x = 5.
On the graph the V-shape lies below the horizontal line between x = −1 and x = 5. Because the inequality is strict (<), the endpoints are not included. So Jalen should use a graph showing the V with vertex (2, −1) and the line y = 2, and indicate the solution as the open interval (−1, 5) on the x-axis.
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