Special Cases for Equations

Front

What is a special case in equations?

Back

A special case in equations refers to scenarios where the equation has either no solutions or infinitely many solutions, rather than a single unique solution.

Front

Solve: 5x + 4 = 5x − 3

Back

no solutions

Front

What does it mean when an equation has no solutions?

Back

It means that there is no value for the variable that can make the equation true.

Front

Solve: 10x + 3 + 3x = 5x + 1 + 8x + 2

Back

infinitely many solutions

Front

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

Back

It means the equation is always TRUE when any value is substituted in for the variable.

Front

Solve: 2y − 3 = 2y − 3

Back

infinitely many solutions

Front

Solve: 6(y + 4) = 6y + 10

Back

no solutions

Front

What is the first step in solving linear equations?

Back

The first step is to simplify both sides of the equation, if possible, by combining like terms.

Front

What is the significance of the variable in an equation?

Back

The variable represents an unknown value that we are trying to solve for.

Front

What does it mean if two expressions are equivalent?

Back

It means that they have the same value for all values of the variable.