One, None, Infinite Solutions

Front

What does it mean if an equation has one solution?

Back

It means there is exactly one value of the variable that satisfies the equation.

Front

What does it mean if an equation has no solutions?

Back

It means there is no value of the variable that can satisfy the equation.

Front

What does it mean if an equation has infinitely many solutions?

Back

It means there are countless values of the variable that satisfy the equation, often because the equation simplifies to a true statement.

Front

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

Back

x = 0.

Front

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

Back

Infinitely many solutions.

Front

What property is used when you subtract the same number from both sides of an equation?

Back

Subtraction Property of Equality.

Front

What property is used when you add the same number to both sides of an equation?

Back

Addition Property of Equality.

Front

What property is used when you multiply both sides of an equation by the same number?

Back

Multiplication Property of Equality.

Front

What property is used when you divide both sides of an equation by the same number?

Back

Division Property of Equality.

Front

If 3x + 15 = 3(x + 5), what is the solution?

Back

Infinitely Many Solutions.