Solving Equations: Special Cases (menu)

Front

What is the definition of one solution?

Back

There will only be ONE number that will make both sides equal.

Front

What is the definition of no solution?

Back

No matter how many different numbers you substitute for the variable, both sides will NEVER be equal.

Front

What is the definition of infinitely many solutions?

Back

You can put any number into the equation and both sides will be TRUE.

Front

Solve the equation: -4(3x + 2) = 3(-4x + 5)

Back

No Solution

Front

What does it mean if an equation has no solution?

Back

It means that there are no values for the variable that will satisfy the equation.

Front

What does it mean if an equation has one solution?

Back

It means there is exactly one value for the variable that makes the equation true.

Front

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

Back

It means that any value for the variable will satisfy the equation.

Front

Example of an equation with no solution:

Back

2x + 3 = 2x + 5 (Both sides cannot be equal for any x)

Front

Example of an equation with one solution:

Back

x + 2 = 5 (x = 3 is the only solution)

Front

Example of an equation with infinitely many solutions:

Back

2x + 4 = 2(x + 2) (Both sides are always equal for any x)