one, none infinite solutions

Front

What does it mean if an equation has one solution?

Back

An equation has one solution when there is exactly one value of the variable that makes the equation true.

Front

What does it mean if an equation has no solutions?

Back

An equation has no solutions when there is no value of the variable that can satisfy the equation.

Front

What does it mean if an equation has infinitely many solutions?

Back

An equation has infinitely many solutions when any value of the variable makes the equation true.

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

Back

No solution.

Front

Example of an equation with infinitely many solutions: x + 4 = x + 4. What is the solution?

Back

Infinitely many solutions.

Front

What is the significance of the equation 10 = 10 in terms of solutions?

Back

It indicates that the equation is always true, meaning it has infinitely many solutions.

Front

How can you determine if an equation has no solutions?

Back

If simplifying the equation leads to a false statement, such as 5 = 3, it has no solutions.

Front

What is the first step in solving an equation to find its solutions?

Back

Isolate the variable on one side of the equation.

Front

What does it mean if two equations are equivalent?

Back

Two equations are equivalent if they have the same solution set.