One, None, Infinite Solutions

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 does it mean if an equation has one solution?

Back

It means there is exactly one value for the variable that makes the equation true.

Front

What does it mean if an equation has no solutions?

Back

It means there is no value for 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 for the variable that satisfy the equation, often because the equation simplifies to a true statement.

Front

Solve: 5x + 4 = 2x + 4

Back

x = 0 (One solution).

Front

Solve: 2x + 4 = 2x + 4

Back

Infinitely many solutions.

Front

Solve: 3x + 15 = 3(x + 5)

Back

Infinitely many solutions.

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 Distributive Property?

Back

a(b + c) = ab + ac; it allows you to multiply a single term by each term inside a parenthesis.

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.