Essential Vocaublary-Solving Equations & Special Solutions

One Solution

Characteristic: Only ONE number will solve the equation.

Infinite Solutions

Characteristic: An equation that has identical variable terms and identical constant terms when simplified.

No Solution

Characteristic: An equation that has identical variable terms but different constant terms.

No Solution

Characteristic: An equation that will simplify down to zero equals a non-zero value.

Infinite Solutions

Characteristic: Any real number will solve the equation.

One Solution

Characteristic: If when solving an equation the answer is x=(any real number), you will have only 1 answer.

Infinite Solutions

Characteristic: If when solving an equation the answer is x=x (where x is any value), you will have infinite answers.

No Solution

Characteristic: If when solving an equation, the answer is x=y (where x is one value and y is a different value), you will have no answer.

One Solution

Characteristic: The variable will equal one number, which can be any real number.

No Solution

Characteristic: There are zero solutions to the equation.

One Solution

Definition: A single value substituted in for the variable (such as x) that makes the equation true.

Infinite Solutions

Definition: Any value substituted in for the variable (such as x) will make the equation true.

No Solution

Definition: No value substituted in for the variable (such as x) will make the equation true; also referred to as a null set.

No Solution

What it LOOKS LIKE... The equation will have a different value on either side of the equal sign/=.

Infinite Solutions

What it LOOKS LIKE... The equation will have the same value on either side of the equal sign/=.

One Solution

What it LOOKS LIKE... The equation will have the variable on one side of the equation and the constant on the other side.