Solving Equations (one, many or no solutions)

Front

What is the definition of 'one solution'?

Back

There is only ONE number you can plug in for the variable to make the equation true.

Front

What is the definition of 'no solution'?

Back

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

Front

What is the definition of 'infinite solutions'?

Back

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

Front

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

Back

Infinite Solutions

Front

Solve the equation: 5x + 6 = 2 + 3x

Back

One Solution

Front

Solve the equation: 3r - 5 = 2r

Back

One Solution

Front

What does it mean if an equation has no solution?

Back

The equation is inconsistent; there are no values for the variable that satisfy it.

Front

What does it mean if an equation has infinite solutions?

Back

The equation is an identity; it holds true for all values of the variable.

Front

How can you determine if an equation has one solution?

Back

If you can isolate the variable and find a specific value that satisfies the equation.

Front

Example of an equation with no solution: 2x + 3 = 2x + 5

Back

No Solution (the same variable cancels out, leading to a false statement).