Solving Equations with Special Cases

Front

What is an equation with infinitely many solutions?

Back

An equation that is true for all values of the variable, often resulting from equivalent expressions on both sides.

Front

What value of n in the equation 3(10x + 5) = 30x + n creates infinitely many solutions?

Back

n = 15.

Front

What does it mean if an equation has no solution?

Back

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

Front

Solve the equation: 4(r + 2) - 3 = 4r - 11. Does it have a solution?

Back

No Solution.

Front

What does it mean if an equation has many solutions?

Back

It means there are infinitely many values for the variable that satisfy the equation.

Front

Solve the equation: 3(x - 11) = 5 + 3x. Does it have a solution?

Back

No Solution.

Front

Solve the equation: 3(2x - 8) = 2(3x - 12). Does it have a solution?

Back

Many Solutions.

Front

Solve the equation: 5(3x - 6) = 3(5x - 10). Does it have a solution?

Back

Many Solutions.

Front

What is the first step in solving an equation?

Back

Isolate the variable by performing inverse operations.

Front

What is a special case in solving equations?

Back

A situation where the equation simplifies to a true statement (many solutions) or a false statement (no solution).