One Solution, No Solution, Many 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 solution?

Back

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

Front

What does it mean if an equation has many solutions?

Back

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

Front

Example of an equation with one solution: 3x = x + 4. What is the solution?

Back

x = 2.

Front

Example of an equation with no solution: 6x - 3 = 6x + 9. Why does it have no solution?

Back

Both sides simplify to 6x, leading to -3 = 9, which is false.

Front

Example of an equation with many solutions: 28a - 4 = 28a - 4. Why does it have many solutions?

Back

Both sides are identical, so any value of 'a' satisfies the equation.

Front

What is the first step to determine the number of solutions for an equation?

Back

Simplify the equation as much as possible.

Front

If an equation simplifies to a true statement like 0 = 0, how many solutions does it have?

Back

It has many solutions.

Front

If an equation simplifies to a false statement like 0 = 5, how many solutions does it have?

Back

It has no solution.

Front

What is the significance of the coefficients in determining the number of solutions?

Back

Coefficients help identify if the equations are equivalent or if they lead to contradictions.