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Solving Linear Equations with Grouping Symbols and Fractions

Solving Linear Equations with Grouping Symbols and Fractions
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2012-09-29 15:00
VectorFunctionCoordinate GeometryGeometric ConstructionGraphing
This GeoGebra example demonstrates solving linear equations within a geometric context, emphasizing grouping symbols and fraction handling. Key math concepts include linear equation solving techniques, fraction arithmetic, isolation of variables in literal equations, and algebraic manipulation. Construction highlights: utilizes Polygon for creating polygonal shapes, Segment for drawing lines, If for conditional step logic, PointIn for interactive point checks, Point and Vector for coordinate and direction management, and Sequence for generating step-by-step sequences. Objects such as row4Step3 and solveHead facilitate a guided solution process, making it suitable for middle or high school mathematics education on equation solving.

GeoGebra Commands & Parameters

  1. Polygon((0, -1.5), (4, -1.5), (4, 3), (0, 3)) → row4Step3, i, j, k, l
  2. Polygon((-1.5, 0), (9.5, 0), (9.5, 6), (-1.5, 6)) → row2Step1, e, f, g, b_3
  3. Polygon((0, 3), (4, 3), (4, 5), (0, 5)) → row3step2, m, n, p, q
  4. Polygon((4, -1.5), (9.5, -1.5), (9.5, 0), (4, 0)) → row2Check, r, s, checkBottomDivider, a_1
  5. Polygon((0, 6), (9.5, 6), (9.5, 7), (0, 7)) → row1Header, a_2, b, c, d
  6. Segment((x(Corner[solve2a_1, 1]), 2.1), (x(Corner[solve1_2, 2]), 2.1)) → step2segment
  7. If(b_4 - h ≟ 0 ∧ (a ≠ -constR) ∨ solution ≟ Infinity, true, false) → notValid
  8. Segment((4, 5), (4, 7)) → segmentDivider
  9. Segment((x(Corner[solve2a_1, 1]), 0), (x(Corner[solve1_2, 2]), 0)) → step3segment
  10. PointIn(Polygon[(5.5, 2), (10, 2), (10, 4), (5.5, 4)]) → E
  11. PointIn(Polygon[(5.5, 0.5), (10, 0.5), (10, 1.5), (5.5, 1.5)]) → B
  12. Point(Segment[B + (0.5, 0), (11, y(B))]) → C
  13. Point(Segment[E + (0.5, 0), (11, y(E))]) → D
  14. Segment(Midpoint[B, C], (x(Midpoint[B, C]), y(D))) → height
  15. Polygon(B, C, D, E) → trap, b_1, trapR, b_2, trapL
  16. Vector((If[x(C) > x(D), x(C), x(D)], y(C)) + (0.25, (y(D) - y(C)) / 2 + 0.1), (If[x(C) > x(D), x(C), x(D)], y(C)) + (0.25, 0)) → heightVectorBottom
  17. Vector((If[x(C) > x(D), x(C), x(D)], y(C)) + (0.25, (y(D) - y(C)) / 2 - 0.1), (If[x(C) > x(D), x(C), x(D)], y(D)) + (0.25, 0)) → heightVectorTop
  18. Segment((3.5, 5), (10.5, 5)) → checkTopDivider
  19. Sequence(Segment[(5.5 + i, 0), (5.5 + i, 5)], i, 0, 6, 0.5) → gridV
  20. Sequence(Segment[(5, 0.5 + i), (12, 0.5 + i)], i, 0, 4, 0.5) → gridH