Properties of Equality Warmup

x = x

• Transitive Property of Equality

• Symmetric Property of Equality

• Reflexive Property of Equality

• Division Property of Equality

Answer explanation

The statement x = x illustrates the Reflexive Property of Equality, which states that any quantity is equal to itself. This property is fundamental in mathematics and confirms that x is equal to x.

Tags

CCSS.7.EE.A.1

Kai is solving an equation and reaches Step 2. Step 2 is what?

• Substitution property (simplify)

• Multiplication property of equality

• Division property of equality

• Distributive Property

Answer explanation

In Step 2, the Distributive Property is applied to simplify expressions by distributing a multiplier across terms within parentheses, making it the correct choice for this step in solving the equation.

Tags

CCSS.8.EE.C.7B

David has 5 apples and gives 2 to Sophia. What is the step to find out how many apples David has left?

• Substitution property (simplify)

• Addition property of equality

• Subtraction property of equality

Answer explanation

To find out how many apples David has left after giving 2 to Sophia, we use the subtraction property of equality. We subtract the 2 apples given from the 5 apples he originally had.

Tags

CCSS.HSA.REI.A.1

Identify the property:

If 31 = 2x - 5, then 2x - 5 = 31

• Reflexive

• Symmetric

• Transitive

• Substitution

Answer explanation

The symmetric property states that if one quantity equals another, then the second equals the first. Here, if 31 = 2x - 5, it follows that 2x - 5 = 31, confirming the symmetric property.

For any numbers a, b, and c, if a = b and b = c, then a = c.

• Transitive Property of Equality

• Symmetric Property of Equality

• Transitive Property of Congruence

• Symmetric Property of Congruence

Answer explanation

The statement a = b and b = c implies that a and c are equal, which is the essence of the Transitive Property of Equality. This property states that if one quantity equals a second, and the second equals a third, then the first equals the third.

Identify the property you would use to solve this equation:
4x = 72

• Addition Property of Equality

• Subtraction Property of Equality

• Multiplication Property of Equality

• Division Property of Equality

Answer explanation

To solve the equation 4x = 72, you would use the Division Property of Equality. This property states that if you divide both sides of the equation by the same non-zero number, the equality remains true. Here, dividing both sides by 4 isolates x.

Tags

CCSS.HSA.REI.A.1

Name the property you will first use to solve this equation:
4x – 5 = 17

• Addition Property of Equality

• Subtraction Property of Equality

• Multiplication Property of Equality

• Division Property of Equality

Answer explanation

To solve the equation 4x – 5 = 17, you first need to isolate the variable x. You can do this by adding 5 to both sides, which is the Addition Property of Equality. This property states that if you add the same number to both sides of an equation, the equality remains true.

Tags

CCSS.HSA.REI.A.1