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: x + 2 = x + 2. What is the solution?

Back

Infinitely many solutions.

Front

What does it mean if two equations are equivalent?

Back

They have the same solution set.

Front

How can you determine if an equation has no solution?

Back

If simplifying the equation leads to a false statement, such as 0 = 5.

Front

How can you determine if an equation has infinitely many solutions?

Back

If simplifying the equation leads to a true statement, such as 0 = 0.

Front

What is the first step in solving the equation 3x + 15 = 3(x + 5)?

Back

Distribute the 3 on the right side: 3x + 15 = 3x + 15.