Vocabulary

Null Set: Empty set. Symbol is ∅ or {}

Identity: An equation that is true for every value for the variable.

Concept

Determine if the solution to equations are null set or identity.

Rules

Need to simplify before solving

1. Distribute if necessary
2. Gather like terms on each side of the equation

Then solve.

1. Gather the variable terms together
2. Isolate the variable term
3. Isolate the variable.

Example

Determine whether the result when solving the corresponding equation is the null set or identity.

3x - 2 + x = 4x + 2 

Solution

3x - 2 + x = 4x + 2 

4x - 2 = 4x + 2

-2 ≠ 2

Answer: ∅ or Null Set

Pre-requisite Skills

Solve Two-Step Equations (8.2.2)

Solve Two-Sided Equations with Rational Coefficients (8.2.4)

Solve Complex Equations (7.6.5)