One Solution, No Solution, Many Solutions

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What does it mean if an equation has 'No Solution'?

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An equation has 'No Solution' when there are no values that can satisfy the equation. This often occurs when simplifying leads to a contradiction, such as 0 = 5.

Tags

CCSS.8.EE.C.7A

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What does it mean if an equation has 'One Solution'?

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An equation has 'One Solution' when there is exactly one value that satisfies the equation. For example, the equation 2x = 8 has one solution: x = 4.

Tags

CCSS.6.EE.B.7

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

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An equation has 'Many Solutions' when any value can satisfy the equation. This typically occurs when both sides of the equation are identical, such as x = x.

Tags

CCSS.8.EE.C.7A

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Solve the equation: 4y + 5 = 4y - 7

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No Solution

Tags

CCSS.8.EE.C.7A

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Solve the equation: 3x = x + 4

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One Solution: x = 2

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Solve the equation: 3z + 8 = 2 + 3z

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No Solution

Tags

CCSS.8.EE.C.7A

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Solve the equation: Z = Z

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Many Solutions

Tags

CCSS.8.EE.C.7B

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What is an example of an equation with 'No Solution'?

Back

An example is 2x + 3 = 2x - 5, which simplifies to 3 = -5.

Tags

CCSS.8.EE.C.7A

Front

What is an example of an equation with 'One Solution'?

Back

An example is x + 2 = 5, which has the solution x = 3.

Tags

CCSS.6.EE.B.7

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What is an example of an equation with 'Many Solutions'?

Back

An example is 5(x + 1) = 5x + 5, which simplifies to 5 = 5.

Tags

CCSS.8.EE.C.7A