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Understanding Algebraic Equations with Tile Models

Learn how algebra tiles can aid in solving equations and understand concepts like isolating variables and using zero pairs. Explore Distributive Property through practical examples and solve equations step by step.

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Understanding Algebraic Equations with Tile Models

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  1. Solving Equations • Algebra tiles can be used to explain and justify the equation solving process. The development of the equation solving model is based on two ideas. • Variables can be isolated by using zero pairs. • Equations are unchanged if equivalent amounts are added to each side of the equation.

  2. Solving Equations • Use the green rectangle as X and the red rectangle (flip-side) as –X (the opposite of X). X + 2 = 3 2X – 4 = 8 2X + 3 = X – 5

  3. Solving Equations X + 2 = 3 2X – 4 = 8

  4. Solving Equations 2X + 3 = X – 5

  5. Distributive Property • Use the same concept that was applied with multiplication of integers, think of the first factor as the counter. • The same rules apply. 3(X+2) • Three is the counter, so we need three rows of (X+2)

  6. Distributive Property 3(X + 2) 3(X – 4) -2(X + 2) -3(X – 2)

  7. Find the solution of LEOV below. • 2x +5 = x + 4 • 6x + 8 = 5x – 3 • 2x – 5 = 3x + 4 • 11x – 3 = 12x -9 • 2 (x + 1) = 3 (x – 4) • 4( 3 + 2x) = 9(x – 4) • 12 – 14x = 15 – 13x • 8 (x – 2) + 2(2x-1) = 3(3x-3) + 2(x+1) • 7(2x + 1) -3(4x – 5) = x + 8 • 2x ( 3x +1) = 3x (1 + 2x) -1

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