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Mastering Algebra: Distributive Property and Equations Solver

Explore the Distributive Property, solve equations, and practice expansion boxes in this interactive algebra lesson. From basic equations to complex expressions, enhance your skills and understanding step by step.

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Mastering Algebra: Distributive Property and Equations Solver

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  1. Algebra – 2.13 FOCUS ON THE DISTRIBUTIVE PROPERTY

  2. What’s wrong here?Solving: 40 – 4(x + 3) = 7x – 5

  3. Remember expansion boxes? • Multiply: 327 x 6: • Add: 1800 + 120 + 42 = 1962

  4. Use them to visualize the Distributive Property • 7(3x – 4)

  5. Use expansion boxes to expand these expressions: • 3(16 – 2x) • 7 – 5(y – 11) • 2(3z + 1) – (z – 6) • 11(a + 5b – 3c)

  6. Solve the equations. • 3(16 – 2x) = 12 • 7 – 5(y – 11) = 27 • 2(3z + 1) – (z – 6) = 40 • 5(j – 3) = 10(j – 2) • -(s + 2) = 4(s + 1) • -(z + 2/3) = z • 2(2x + 1) – 3(x – 5) = 18

  7. What’s wrong with this? • Using expansion boxes or some other method, show that (a+b)2 does not necessarily equal a2 + b2.

  8. Use this array to show that4(a+b) = 4a + 4b a a a a b b b b Create an array that shows that7(x+y+z) = 7x + 7y + 7z

  9. 2C REFLECTIONS • Determine whether x = -3 is a solution: • 4x + 1 = 2x – 5 x – 4 = -2x • 2(x + 1) + 5 = x + 2 2x + 3 – 4x = -3x • Solve each equation:

  10. MORE REFLECTIONS • How can you solve an equation for which backtracking does not work? • How can you visualize an equation using the number line? What about shapes? Try, for example: 5x = x + 24

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