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Unit 06 · Expressions and EquivalenceLesson

Day 089Proving or Disproving Equivalence

LearnClassworkAnswer keyPDF packet ↗
Standards 6.EE.A.4
LEARNING TARGET

I can justify whether expressions are equivalent.

01 · LEARN

Build the idea

Use operation properties to rewrite an expression. Matching values at one input do not prove equivalence for all inputs. A single counterexample is enough to show two expressions are not equivalent.

WORKED EXAMPLE 1

Are 7(x + 3) and 7x + 21 equivalent for every x? Use a property or a counterexample.

Yes; distribution gives 7x + 21

7(x + 3) = 7x + 21. This matches.

WORKED EXAMPLE 2

Are 2(x + 5) and 2x + 10 equivalent for every x? Use a property or a counterexample.

Yes; distribution gives 2x + 10

2(x + 5) = 2x + 10. This matches.

02 · PRACTICE

Your turn

Work in order. Start with the foundations, then build toward explanation and application.

  1. Are 8(x + 5) and 8x + 5 equivalent for every x? Use a property or a counterexample.

  2. Are 4(x + 4) and 4x + 16 equivalent for every x? Use a property or a counterexample.

  3. Are 8(x + 2) and 8x + 2 equivalent for every x? Use a property or a counterexample.

  4. Are 5(x + 3) and 5x + 15 equivalent for every x? Use a property or a counterexample.

  5. Are 7(x + 5) and 7x + 5 equivalent for every x? Use a property or a counterexample.

  6. Are 7(x + 2) and 7x + 14 equivalent for every x? Use a property or a counterexample.

  7. Are 4(x + 3) and 4x + 3 equivalent for every x? Use a property or a counterexample.

  8. Are 6(x + 5) and 6x + 30 equivalent for every x? Use a property or a counterexample.

  9. Are 5(x + 7) and 5x + 7 equivalent for every x? Use a property or a counterexample.

  10. Are 2(x + 4) and 2x + 8 equivalent for every x? Use a property or a counterexample.

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. No; at x = 0, values are 40 and 5

    8(x + 5) = 8x + 40. The constants 40 and 5 differ.

  2. Yes; distribution gives 4x + 16

    4(x + 4) = 4x + 16. This matches.

  3. No; at x = 0, values are 16 and 2

    8(x + 2) = 8x + 16. The constants 16 and 2 differ.

  4. Yes; distribution gives 5x + 15

    5(x + 3) = 5x + 15. This matches.

  5. No; at x = 0, values are 35 and 5

    7(x + 5) = 7x + 35. The constants 35 and 5 differ.

  6. Yes; distribution gives 7x + 14

    7(x + 2) = 7x + 14. This matches.

  7. No; at x = 0, values are 12 and 3

    4(x + 3) = 4x + 12. The constants 12 and 3 differ.

  8. Yes; distribution gives 6x + 30

    6(x + 5) = 6x + 30. This matches.

  9. No; at x = 0, values are 35 and 7

    5(x + 7) = 5x + 35. The constants 35 and 7 differ.

  10. Yes; distribution gives 2x + 8

    2(x + 4) = 2x + 8. This matches.

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