How many solutions??

Front

What does it mean when an equation has one solution?

Back

It means that there is exactly one value of the variable that satisfies the equation.

Front

What does it mean when an equation has no solution?

Back

It means that there is no value of the variable that can satisfy the equation, often because the equation represents a contradiction.

Front

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

Back

It means that there are countless values of the variable that satisfy the equation, often because the equation is an identity.

Front

What is an example of an equation with one solution?

Back

An example is 2 = X, where X = 2.

Front

What is an example of an equation with no solution?

Back

An example is 4 = 8, which is a contradiction.

Front

What is an example of an equation with infinitely many solutions?

Back

An example is -5 = -5, which is always true.

Front

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

Back

By simplifying the equation and analyzing the resulting statements.

Front

What is the significance of the equation X = 0 in terms of solutions?

Back

It indicates that there is one specific solution, which is X = 0.

Front

What type of solution does the equation 3X + 2 = 3X + 5 have?

Back

It has no solution, as simplifying leads to a contradiction (2 = 5).

Front

What type of solution does the equation 2X + 3 = 2X + 3 have?

Back

It has infinitely many solutions, as it is true for all values of X.