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 infinite solutions?

Back

An equation that is true for all values of the variable, meaning any number can satisfy it.

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 - 3. 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

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 infinite 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 infinite solutions?

Back

By simplifying the equation and analyzing the resulting statements.

Front

Solve the equation: 4x - 5 = 3x + 2. What is the solution?

Back

x = 7.