One Solution, No Solution, Infinite Solutions

Front

What is the definition of one solution?

Back

Only this ONE solution will make the equation true.

Front

What is the definition of no solution?

Back

No matter what constant is substituted in for the variable, the equation will NEVER be true.

Front

What is the definition of infinite solutions?

Back

No matter what constant is substituted in for the variable, the equation is ALWAYS true.

Front

Solve for r: 3r - 5 = 2r

Back

r = 5

Front

Solve for x: 12 (x + 3 ) = 4 (2x + 9 ) + 4x

Back

Infinite Solutions

Front

What does it mean if an equation has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if an equation has infinite solutions?

Back

The lines representing the equations are the same, meaning they overlap completely.

Front

Example of an equation with infinite solutions:

Back

2x + 4 = 2(x + 2) (This simplifies to the same equation.)

Front

Example of an equation with no solution:

Back

x + 2 = x + 3 (This simplifies to a false statement.)

Front

What is the first step to solve an equation?

Back

Isolate the variable on one side of the equation.