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Name Date Student Exploration: Absolute Value Equations Directions Follow the Instructions to go through the simulation Respond be the cured prompts in the orange bases Vocabulary: absolute value, compound inequality, equation, inequality, situation Prior Knowledge Questions (Do these BEFORE using the Gumo.) The solution of an equation like x * 2 = 5 is the value(s) of x that make the equation true. " Hand draw in 1. What is the solution of x + 2 - 57 or click here to we use the drawing X+2-2.5- 2 X:3 2. An equation like x + 2 = 5 can be solved graphically too Graph each side of the equation (y = x * 2 and y = 5) on the grid to the right. A. What is the intersection point? ( 3, 5 B. Which coordinate is the solution, x or y? the X coordinate is the solution Gizmo Warm-up You can solve equations by graphing each side, as you did above. In the Absolute Value Equations and Inequalities Gizmo, you will use graphs to find the solutions of equations and inequalities that involve absolute value, the distance a quantity is from 0 on a number line On the CONTROLS tab in the Gizmo, set a to 1, b to 0, c to 2, and select =. (To quickly set the value of a slider, type the number into the text box to the right of the slider and press Enter.) Notice that each side of jx) = 2 is graphed (y = [x] and y = 2). 1. Look at the graph of y = |x). What is the shape of this graph? 2. Because absolute value is a distance, it is never negative, How does this relate to the shape of the graph of y = kx|? 3. Look at the graphs of y = (x/ and y = 2. What values of x make It equal to 2