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 does it mean if an equation has no solution?

Back

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

Front

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

Back

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

Front

Translate the statement into an equation: Five less than a number is 6.

Back

n - 5 = 6

Front

Solve: 3r - 5 = 2r.

Back

r = 5

Front

Solve: 2x + 1 = 2x - 1.

Back

No Solution

Front

What is the first step to solve the equation 2x + 1 = 2x - 1?

Back

Subtract 2x from both sides.

Front

What is the result of subtracting 2x from both sides of the equation 2x + 1 = 2x - 1?

Back

1 = -1, which is a contradiction.

Front

If an equation simplifies to a true statement like 0 = 0, what does it indicate?

Back

It indicates that there are infinitely many solutions.

Front

If an equation simplifies to a false statement like 1 = 2, what does it indicate?

Back

It indicates that there is no solution.