Justifying Equations with properties

Dr. Arrington solved the equation shown below.

Given: 5(x + 1) - 3(x -2) = 13

Step 1: 5x + 5 - 3x + 6 = 13

Step 2: 5x - 3x + 5 + 6 = 13

Step 3: 2x + 11 = 13

Step 4: 2x + 11 - 11 = 13 - 11

Step 5: 2x = 2

Answer: x = 1

Which properties did he apply from step 1 to step 2?

• Associative pro

• Distributive property

• Subtraction property

• Commutative property

• S1: Mult. poe

  S2: Add. poe

  S3: CLT

  S4: Division poe

• S1: Distributive prop

  S2: Subtract. poe

  S3: Add. poe

  S4: Division poe

• S1: Distributive prop

  S2: Add. poe

  S3: Subtract. poe

  S4: Division poe

• S1: Mult. poe

  S2: Subtract. poe

  S3: CLT

  S4: Division poe

Dr. Arrington has 2 apples and gives 7 apples to Mr. Hollar. Which property justifies the third step?
         2 - 7 = 3x + 7 - 7
          2 - 7 = 3x + 0
          2 - 7 = 3x

• Inverse Property of Addition

• Subtraction Property of Equality

• Commutative Property of Addition

• Identity Property of Addition

Dr. Arrington has 2 apples and gives 7 apples to Mr. Hollar. How many apples does Dr. Arrington have now?
          2 - 7 = 3x + 7 - 7
          2 - 7 = 3x + 0

• Addition Property of Equality

• Opposite Property of Mathematics

• Inverse Property of Addition

• Identity Property of Addition

Mr Hollar is solving an equation and moves from Step 1 to Step 2. Which property justifies the work between Step 1 and Step 2?

• Inverse Property of Multiplication

• Identity Property of Multiplication

• Multiplication Property of Equality

• Division Property of Equality

Mrs. Smith is solving an equation and wants to justify her steps. Which property justifies the work in solving this equation?

• Addition Property of Equality

• Additive Inverse Property

• Identity Property of Addition

• Subtraction Property of Equality

Move a property into each box of the reason column to justify each step.

f

b

h

d

Division Property of Equality

Reflexive Property of Equality

Multiplication Property of Equality

Commutative Property

Subtraction Property of Equality

Addition Property of Equality

Distributive Property

Associative Property

Identify the property of equality.
B=B

• Reflexive Property

• Symmetric Property

• Transitive Property

• Substitution Property

Identify the property of equality.

If a = b and b = c, then a = c

• Transitive Property         
• Symmetric Property
• Reflexive Property
• Substitution Property

Jake earns $5 per hour mowing lawns. How many hours must he work to earn $40? Which equation would help you find the number of hours?

• 5 + x = 40

• 5 - x = 40

• x ÷ 5 = 40

• 5x = 40