One Solution, No Solution, Many Solutions

Front

What does it mean if an equation has 'Many Solutions'?

Back

An equation has 'Many Solutions' if it is true for all values of the variable. For example, the equation Z = Z is true for any value of Z.

Tags

CCSS.8.EE.C.7A

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. For example, the equation 3x = 9 has one solution: x = 3.

Tags

CCSS.6.EE.B.7

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. For example, the equation 6x - 3 = 6x + 9 has no solution.

Tags

CCSS.8.EE.C.7A

Front

Example of an equation with 'Many Solutions':

Back

2x + 9 = 2x + 9.

Tags

CCSS.8.EE.C.7A

Front

Example of an equation with 'One Solution':

Back

3x = 9.

Tags

CCSS.6.EE.B.7

Front

Example of an equation with 'No Solution':

Back

18a + 45 = 18a - 37.2.

Tags

CCSS.8.EE.C.7A

Front

What is the general form of an equation with 'Many Solutions'?

Back

An equation where both sides are identical, such as a = a.

Tags

CCSS.8.EE.C.7A

Front

What is the general form of an equation with 'One Solution'?

Back

An equation that can be simplified to a single value, such as x + 5 = 10.

Tags

CCSS.8.EE.C.7A

Front

What is the general form of an equation with 'No Solution'?

Back

An equation that simplifies to a contradiction, such as 0 = 5.

Tags

CCSS.8.EE.C.7A

Front

How can you identify an equation with 'Many Solutions'?

Back

If you can manipulate the equation and find that both sides are always equal regardless of the variable's value.

Tags

CCSS.8.EE.C.7A