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

Solve: 2x + 1 = 2x - 1

Back

No Solution

Tags

CCSS.8.EE.C.7A

Front

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

Back

Infinitely Many Solutions

Tags

CCSS.8.EE.C.7A

Front

Solve: 3(x-2) + 1 = 3x - 5

Back

Infinite Solutions

Tags

CCSS.8.EE.C.7A

Front

Solve: 6m + 18 = 2m + 18

Back

One Solution

Front

What is the first step to determine the number of solutions for an equation?

Back

Simplify the equation as much as possible to see if it leads to a contradiction or a true statement.

Tags

CCSS.8.EE.C.7A

Front

If an equation simplifies to a statement like 0 = 0, what does that indicate?

Back

It indicates that there are infinite solutions.

Tags

CCSS.8.EE.C.7A

Front

If an equation simplifies to a statement like 5 = 3, what does that indicate?

Back

It indicates that there is no solution.

Tags

CCSS.8.EE.C.7A