One Solution, No Solution, Infinite Solutions

Front

What does 'one solution' mean in an equation?

Back

Only this ONE solution will make the equation true.

Front

What does 'no solution' mean in an equation?

Back

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

Front

What does 'infinitely many solutions' mean in an equation?

Back

The equation is true for an infinite number of values of the variable.

Front

Solve: 2x + 1 = 2x - 1

Back

No Solution

Front

Solve: 3x + 15 = 3(x + 5)

Back

Infinitely Many Solutions

Front

Solve: 6x + 9 – x = 3x + 9 + x

Back

No Solution

Front

What is an example of an equation with one solution?

Back

x + 2 = 5 (Solution: x = 3)

Front

What is an example of an equation with no solution?

Back

2x + 3 = 2x - 1 (No value of x will satisfy this equation.)

Front

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

Back

2(x + 1) = 2x + 2 (True for all x.)

Front

How can you determine if an equation has no solution?

Back

If simplifying leads to a false statement, like 0 = 5.