Solving Equations and Justifying with Properties

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

Multiplication Property of Equality

Addition Property of Equality

Commutative Property

Associative Property

Division Property of Equality

Subtraction Property of Equality

Distributive Property

Reflexive Property of Equality

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

Mrs. Smith is helping Rohan solve this linear equation for x. Original equation: \(\frac{1}{2}\left(x+6\right)\ =\ -\frac{3}{2}x+5\) Step 1: \(\frac{1}{2}x+3\ =-\frac{3}{2}x+5\) Step 2: 2x + 3= 5 Step 3: 2x = 2 Step 4: x =1 Step 5: 2x = 2 Answer: x = 1 Which properties did she apply from step 1 to step 2?

• 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

Identify the property of equality.

• Transitive Property         

• Symmetric Property

• Reflexive Property

• Substitution Property

B=B

• Reflexive Property

• Symmetric Property

• Transitive 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

Which of the following situations could be descried by the equation y= -25x + 120

• There are 120 people in the football stadium, and 25 more are entering each hour.

• A plumber charges $25 for a house call and $120 per hour.

• A teacher has 120 students. Her third period has 25 students

• There are 120 gallons of water in a tank. It releases water at a rate of 25 gallons per minute

Which property justifies the work between step 1 and step 2?
Step 1: 10-2k=k-5-3k Step 2: 10-2k=-5-2k

• Distributive Property

• Combine Like Terms

• Multiplication Property of Equality

• Division Property of Equality