2.4 One Solution, No Solution, Infinitely Many Solutions

Front

What does it mean if an equation has one solution?

Back

An equation has one solution if there is exactly one value of the variable that makes the equation true.

Front

What does it mean if an equation has no solutions?

Back

An equation has no solutions if there is no value of the variable that can satisfy the equation.

Front

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

Back

An equation has infinitely many solutions if there are countless values of the variable that satisfy the equation, often because the equation simplifies to a true statement.

Front

Solve the equation: −5x + 5 − 4x = −1 − 9x

Back

No Solutions

Front

Solve the equation: 3(−2x − 6) = −6x − 8

Back

No Solutions

Front

Solve the equation: −5 + 7x = 7x + 5

Back

No Solutions

Front

Solve the equation: 4x + 8 = 2(2x + 4)

Back

Infinitely many solutions

Front

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

Back

Infinitely many solutions

Front

What is the property of equality used to solve equations?

Back

The property of equality states that if two expressions are equal to each other, then you can add, subtract, multiply, or divide both sides by the same number without changing the equality.

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed, typically in the form ax + b = c.