Number of Solutions

Front

What is the definition of a solution in mathematics?

Back

A solution is a value or set of values that satisfies an equation.

Front

What does it mean if an equation has one solution?

Back

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

Front

What does it mean if an equation has no solution?

Back

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

Front

What does it mean if an equation has infinite solutions?

Back

It means there are countless values that satisfy the equation, often represented as an identity.

Front

Example of an equation with one solution: 2x + 3 = 7. What is the solution?

Back

x = 2.

Front

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

Back

No solution.

Front

Example of an equation with infinite solutions: 3(x + 2) = 3x + 6. What is the solution?

Back

Infinite solutions.

Front

What is an identity in mathematics?

Back

An identity is an equation that is true for all values of the variable.

Front

If you have the equation 3 = 1/3, what type of solution do you have?

Back

No solution.

Front

If you have the equation 2 = x, what type of solution do you have?

Back

One solution.