one, none, infinitely many solutions

Front

What does it mean if an equation has one solution?

Back

It means there is exactly one value for the variable that makes the equation true.

Front

What does it mean if an equation has no solutions?

Back

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

Front

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

Back

It means that any value substituted for the variable will make the equation true.

Front

Solve for x: 5x + 6 = 2 + 3x

Back

x = -2; one solution.

Front

Solve for r: 3r - 5 = 2r

Back

r = 5; one solution.

Front

Solve for x: -3(4x + 2) = -12x - 6

Back

Infinitely many solutions.

Front

What is the definition of one solution?

Back

Only one specific value of the variable makes the equation true.

Front

What is the definition of no solution?

Back

The equation is contradictory and cannot be satisfied by any value.

Front

What is the definition of infinitely many solutions?

Back

The equation is an identity, true for all values of the variable.

Front

Solve for x: 2x + 3 = 3x - 4

Back

x = 7; one solution.