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Expressions and Equations

Problems

Properties

Solving Equations with a Variable on Both Sides

Problem : Name the property shown:
x = 12 and 12 = y . Thus, x = y

Transitive Property of Equality

Problem : Name the property shown:
4(2x) = 8x

Associative Property of Multiplication

Problem : What number, when multiplied by 3, is equal to 1?

(the reciprocal of 3)

Problem : What number, when multiplied by , is equal to 1?

(the reciprocal of )

Problem : Name the property or operation used in each step:
Solve for x : - 16 = - 4

  1. - 16 = - 4
  2. - 16 + 16 = - 4 + 16
  3. + 0 = 12
  4. = 12
  5. 12() = 12(12)
  6. 1x = 144
  7. x = 144

  1. Given
  2. Addition Property of Equality
  3. Addition
  4. Additive Identity Property
  5. Multiplication Property of Equality
  6. Multiplication
  7. Multiplicative Identity Property

Problem : Name the property or operation used in each step:
Solve for y : 3(4y + 3) = 9

  1. 3(4y + 3) = 9
  2. 12y + 9 = 9
  3. 12y + 9 - 9 = 9 - 9
  4. 12y + 0 = 0
  5. 12y = 0
  6. 12 = 0ory = 0
  7. Since 12âÉ  0 , y = 0

  1. Given
  2. Distributive Property of Multiplication over Addition
  3. Subtraction Property of Equality
  4. Subtraction
  5. Additive Identity Property
  6. Zero Product Property
  7. (inference)

Problem : Name the property or operation used in each step:
Solve for x if y = 4 : 4y + 5 = 3(x + 1)

  1. 4y + 5 = 3(x + 1)
  2. 4(4) + 5 = 3(x + 1)
  3. 16 + 5 = 3(x + 1)
  4. 21 = 3(x + 1)
  5. =
  6. 7 = 1(x + 1)
  7. 7 = x + 1
  8. 7 - 1 = x + 1 - 1
  9. 6 = x + 0
  10. 6 = x
  11. x = 6

  1. Given
  2. Substitution Property
  3. Multiplication
  4. Addition
  5. Division Property of Equality
  6. Division
  7. Multiplicative Identity Property
  8. Subtraction Property of Equality
  9. Subtraction
  10. Additive Identity Property
  11. Symmetric Property of Equality

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