Equations with one solution, no solutions, or infinite

Front

What is an equation with one solution?

Back

An equation that has exactly one value for the variable that makes it true.

Front

What is an equation with no solutions?

Back

An equation that has no value for the variable that can satisfy it, often resulting in a contradiction.

Front

What is an equation with infinitely many solutions?

Back

An equation that is true for all values of the variable, often resulting in 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 solutions: 2x + 4 = 2x + 5. What is the solution?

Back

No solution.

Front

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

Back

Infinitely many solutions.

Front

What does it mean if an equation simplifies to a true statement like 0 = 0?

Back

It indicates that the equation has infinitely many solutions.

Front

What does it mean if an equation simplifies to a false statement like 5 = 0?

Back

It indicates that the equation has no solutions.

Front

How do you determine if an equation has one solution, no solutions, or infinitely many solutions?

Back

By simplifying the equation and analyzing the resulting statement.

Front

What is the first step in solving an equation?

Back

Isolate the variable on one side of the equation.