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Understanding Linear Expressions with Rational Coefficients

Learn to expand linear expressions involving multiplication, addition, and subtraction with rational coefficients. Explore properties of real numbers like distributive, commutative, and associative laws. Practice expanding and simplifying expressions. Dive into combining like terms and utilizing diagrams. Improve your algebra skills with step-by-step explanations.

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Understanding Linear Expressions with Rational Coefficients

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  1. How do you expand linear expressions that involve multiplication, addition, and subtraction? For example, how do you expand 3(4 + 2x)?

  2. In this lesson you will learn how to expand linear expressions with rational coefficients by using the properties of real numbers.

  3. Vocabulary: Linear expression Rational coefficient Combine like terms + 2 = 9v 2v + 3 + 7v - 1

  4. Properties of the Real Numbers: Commutative: 11 + 4 = 4 + 11 Associative: (4 + 3) + 9 = 4 + (3 + 9) Distributive: 5(6 + 2) = 5(6) + 5(2)

  5. Failing to distribute negative numbers completely: -9(4 + 3) = -9(4) + 9(3) -

  6. Distributing multiplication over multiplication: 3(5 2) = 3(5) 3(2) - 3(10) 15 6 - = 90 30

  7. Expand 3(2x + 4) + 4 2x 2x + 4 2x + 4 3 2x + 4 + 3(4) = 6x + 12 3(2x) 3(2x + 4) =

  8. Expand and combine like terms: 11(3a- 2) - 6(8a- 9) = 11(3a- 2) + (-6)(8a- 9) = 11(3a) + 11(-2) + (-6)(8a) + (-6)(-9) + (-48a) + 54 + (-22) = 33a + 32 = -15a

  9. In this lesson you have learned how to expand linear expressions with rational coefficients by using the properties of real numbers.

  10. Simplify: 9(5k - 8) - 4(7 - 2k)

  11. Use a diagram to show why 4(3y + 2) = 12y + 8.

  12. Simplify: 5(7y + 1) - 2(9y - 10) + 3(18 - 4y)

  13. Write at least two different linear expressions that expand and simplify to a value of 40x + 27.

  14. 1. Simplify: 7(3x-4) + 2(5 + 6x) 2. Simplify: 11(4 - 8w) - 6(-9w - 5)

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