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Rules for Solving αx=β

Rules for Solving αx=β
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2012-06-19 13:02
FunctionCoordinate GeometryGeometric Construction
This example helps students understand how to solve the equation αx=β. By adjusting parameters a and b, students can observe the solutions under different conditions. The example uses if, Textfield, Polygon, and other GeoGebra commands, suitable for middle school and above students.

GeoGebra Commands & Parameters

  1. If(-3 < x < 10, 1.2) → p
  2. If(-3 < x < 10, 2.4) → q
  3. If(-3 < x < 10, 3.6) → r
  4. Textfield(num1) → inputBox1
  5. Textfield(num2) → inputBox2
  6. If(num1 ≠ 0, If[b ≟ f, If[b ≟ i, num2 / num1]]) → value
  7. If(b < 3, "Η εξίσωση 0x=" + num2, "Η λύση της " + num1 + "x=" + num2) → part13
  8. If(b ≠ 2, "Η εξίσωση 0x=" + num2, "Η λύση της " + num1 + "x=" + num2) → part12
  9. If(b > 1, "Η εξίσωση 0x=" + num2, "Η λύση της " + num1 + "x=" + num2) → part11
  10. If(g ≟ 3, "είναι ΤΑΥΤΟΤΗΤΑ", If[h ≟ 3, "είναι ΑΔΥΝΑΤΗ", "είναι x=" + num2 + "/" + num1 + "=" + (num2 / num1)]) → part23
  11. If(g ≟ 2, "είναι ΤΑΥΤΟΤΗΤΑ", If[h ≟ 2, "είναι ΑΔΥΝΑΤΗ", "είναι x=" + num2 + "/" + num1 + "=" + (num2 / num1)]) → part22
  12. If(g ≟ 1, "είναι ΤΑΥΤΟΤΗΤΑ", If[h ≟ 1, "είναι ΑΔΥΝΑΤΗ", "είναι x=" + num2 + "/" + num1 + "=" + (num2 / num1)]) → part21
  13. If((num1 ≟ 0 ∧ (b ≠ 3) ∨ (num1 ≠ 0) ∧ b ≟ 3) ∧ (num2 ≟ 0 ∧ (d ≟ 3 ∨ f ≟ 3) ∨ (num2 ≠ 0) ∧ (d ≠ 3)), true, false) → condition3
  14. If((num1 ≟ 0 ∧ (b ≠ 2) ∨ (num1 ≠ 0) ∧ b ≟ 2) ∧ (num2 ≟ 0 ∧ (d ≟ 2 ∨ f ≟ 2) ∨ (num2 ≠ 0) ∧ (d ≠ 2)), true, false) → condition2
  15. If((num1 ≟ 0 ∧ (b ≠ 1) ∨ (num1 ≠ 0) ∧ b ≟ 1) ∧ (num2 ≟ 0 ∧ (d ≟ 1 ∨ f ≟ 1) ∨ (num2 ≠ 0) ∧ (d ≠ 1)), true, false) → condition1
  16. Polygon(Α, Β, Γ, Δ) → πολύγ1, α, β, γ, δ

AI Drawing Prompt Reference

Draw a graph showing the solution of the equation αx=β, where α and β can be adjusted through input boxes. First, draw three parallel lines p, q, and r. Then, based on the values of α and β, display different solution scenarios, including specific values, identity equations, or no solutions. Finally, draw a quadrilateral to represent the solution area.
The prompt above was compiled from the original drawing commands and is for reference only.