Equivalent Transformations of Equations

[size=100]Learn how to visualize equivalent transformations of equations with GeoGebra[br][/size]
Step 1: Try out the GeoGebra applet
[size=100][size=100]Change the value of the slider in order to explore how the lines change[/size][/size].
Step 2: Watch the tutorial video
Step 3: Create the construction yourself
Construction Steps
[table][tr][td]1.[/td][td][/td][td][size=100]In the CAS View, enter the equation [font=Courier New]x - 2 = 1[/font] and hit the Enter key. [/size][br][/td][/tr][tr][td]2.[/td][td][/td][td][size=100]In order to visualize the left side term of the equation, enter [font=Courier New]LeftSide[#1][/font]. Then, click on the Show/Hide symbol to the left of line 2 in order to show the graph in the [i]Graphics View[/i]. [/size][size=100][br][/size][/td][/tr][tr][td][br][/td][td][/td][td][size=100][u]Hint[/u]: The input [i]#1[/i] refers to the output of the row [i]1[/i], so you don’t have to enter the equation again.[/size][/td][/tr][tr][td][table][/table]3.[br][/td][td][/td][td][size=100]Also visualize the right side term of the equation by entering [font=Courier New]RightSide[#1][/font][i] [/i]and showing the graph. [color=#ff0000]Does not work now![/color][/size][/td][/tr][tr][td]4.[br][/td][td][icon]/images/ggb/toolbar/mode_slider.png[/icon][/td][td][size=100]In the Graphics View, create a slider [i]a[/i] using the [i]slider[/i] tool. In the appearing window set the slider name to [i]a = 0[/i] and change the Increment: [i]1[/i]. Then, click [i]Apply[/i].[/size][/td][/tr][tr][td]5.[br][/td][td][/td][td][size=100]In the CAS View, enter [font=Courier New](#1) + a[/font]. [/size][br][/td][/tr][tr][td][br][/td][td][br][/td][td][size=100][u]Hint[/u]: This will allow you to transform the equation using slider [i]a[/i].[/size][br][/td][/tr][tr][td]6.[br][/td][td][/td][td][size=100]Enter [font=Courier New]f_a(x):=f + a[/font] and hit the Enter key. Then, show the graph of this new term.[/size][/td][/tr][tr][td]7.[br][/td][td][/td][td][size=100]Enter [font=Courier New]g_a(x):=g + a[/font] and show the graph of the resulting term.[/size][/td][/tr][tr][td]8.[/td][td][icon]/images/ggb/toolbar/mode_move.png[/icon][/td][td][size=100]In the Graphics View, use the [i][font=Arial]Move[/font][/i] tool in order to simplify the equation by changing the value of the slider.[/size][/td][/tr][/table]
[size=100]How can this example help you understand why equivalent transformations can be applied to an equation? [br][u]Hint[/u]: You might want to show the graph of the equation in row 1 in the Graphics View while exploring how changing the value of slider [i]a[/i] affects the left and right side of the equation and the solution.[/size]

Information: Equivalent Transformations of Equations