Solving Equations: Special Cases

Front

What does it mean if an equation has no solution?

Back

An equation has no solution when there is no value for the variable that makes the equation true, such as 4 = 5.

Front

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

Back

An equation has infinitely many solutions when any value for the variable satisfies the equation, such as x + 2 = x + 2.

Front

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

Back

No Solutions

Front

Solve the equation: 3x - 4 = 3x + 2

Back

No Solutions

Front

Solve the equation: 5n + 10 = 5(n + 2)

Back

Infinitely Many Solutions

Front

What is a special case in solving equations?

Back

A special case occurs when the equation simplifies to a statement that is always true or always false.

Front

Solve the equation: 4x + 1 = 4x + 1

Back

Infinitely Many Solutions

Front

What is the first step in solving an equation?

Back

The first step is to simplify both sides of the equation if possible.

Front

Solve the equation: 7x - 3 = 7x + 2

Back

No Solutions

Front

What does it mean if an equation simplifies to a true statement like 0 = 0?

Back

It means the equation has infinitely many solutions.