One, None, Infinite Solutions

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions when any value of the variable satisfies the equation, meaning the two sides of the equation are always equal.

Front

What does it mean if an equation has one solution?

Back

An equation has one solution when there is exactly one value of the variable that makes the equation true.

Front

What does it mean if an equation has no solutions?

Back

An equation has no solutions when there is no value of the variable that can satisfy the equation, meaning the two sides are never equal.

Front

Example of an equation with infinite solutions: 2x + 4 = 2x + 4. What is the solution?

Back

Infinite solutions.

Front

Example of an equation with one solution: 5x + 4 = 2x + 4. What is the solution?

Back

One solution.

Front

Example of an equation with no solutions: 3x + 2 = 3x + 5. What is the solution?

Back

No solution.

Front

What is the Addition Property of Equality?

Back

If you add the same number to both sides of an equation, the two sides remain equal.

Front

What is the Subtraction Property of Equality?

Back

If you subtract the same number from both sides of an equation, the two sides remain equal.

Front

What is the Distributive Property?

Back

The Distributive Property states that a(b + c) = ab + ac, meaning you can distribute a number across a sum.

Front

What is the Multiplication Property of Equality?

Back

If you multiply both sides of an equation by the same non-zero number, the two sides remain equal.