One Solution, No Solution, Infinite Solutions

Front

What does 'one solution' mean in the context of equations?

Back

An equation has 'one solution' when there is exactly one value of the variable that satisfies the equation.

Tags

CCSS.7.EE.B.4A

Front

What does 'no solution' mean in the context of equations?

Back

An equation has 'no solution' when there are no values of the variable that can satisfy the equation.

Tags

CCSS.8.EE.C.7A

Front

What does 'infinite solutions' mean in the context of equations?

Back

An equation has 'infinite solutions' when there are countless values of the variable that satisfy the equation, often because the equation simplifies to a true statement.

Tags

CCSS.8.EE.C.7A

Front

Example of an equation with one solution: 2x + 3 = 7. What is the solution?

Back

x = 2.

Tags

CCSS.7.EE.B.4A

Front

Example of an equation with no solution: 2x + 4 = 2x + 5. What is the solution?

Back

No solution.

Tags

CCSS.8.EE.C.7A

Front

Example of an equation with infinite solutions: 3(x + 2) = 3x + 6. What is the solution?

Back

Infinite solutions.

Tags

CCSS.8.EE.C.7A

Front

What is the first step to solve the equation 3r - 5 = 2r?

Back

Isolate the variable by subtracting 2r from both sides.

Front

In the equation 6x + 9 - x = 3x + 9 + x, what do you notice about the coefficients of x?

Back

The coefficients simplify to show that the equation has no solution.

Tags

CCSS.8.EE.C.7A

Front

How can you tell if an equation has infinite solutions?

Back

If, after simplifying, both sides of the equation are identical, it has infinite solutions.

Tags

CCSS.8.EE.C.7A

Front

What is the significance of the equation 12(x + 3) = 4(2x + 9) + 4x?

Back

It demonstrates an equation with infinite solutions after simplification.

Tags

CCSS.8.EE.C.7A