One Solution, No Solution, Infinite 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 solution?

Back

An equation has no solution 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.

Front

Solve: 3x + 15 = 3(x + 5)

Back

Infinitely Many Solutions

Front

Solve: 6x + 9 - x = 3x + 9 + x

Back

No Solution

Front

Solve: 2x + 1 = 2x - 1

Back

No Solution

Front

Simplify and determine the solution type: 3x - 7 = 3(x - 3) + 2

Back

Infinitely Many Solutions

Front

What is the first step in solving the equation 3x + 15 = 3(x + 5)?

Back

Distribute the 3 on the right side: 3x + 15 = 3x + 15.

Front

What is the significance of the coefficients in an equation?

Back

Coefficients determine the relationship between the variable and the constant terms in an equation.

Front

How can you identify an equation with no solution?

Back

If simplifying the equation leads to a false statement, such as 0 = 5, it has no solution.