One Solution, No Solution, Many Solutions

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

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An equation has 'Many Solutions' when both sides of the equation are identical, meaning any value for the variable will satisfy the equation.

Tags

CCSS.8.EE.C.7A

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

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An equation has 'No Solution' when it leads to a contradiction, meaning there is no value for the variable that can make the equation true.

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 for the variable that satisfies the equation.

Tags

CCSS.8.EE.C.7A

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Example of an equation with 'Many Solutions': 28a - 4 = 28a - 4. How many solutions does it have?

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Many Solutions

Tags

CCSS.8.EE.C.7A

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Example of an equation with 'No Solution': 6b - 4 = 6b + 4. How many solutions does it have?

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No Solution

Tags

CCSS.8.EE.C.7A

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Example of an equation with 'No Solution': 4y + 5 = 4y - 7. How many solutions does it have?

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No Solution

Tags

CCSS.8.EE.C.7A

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Example of an equation with 'Many Solutions': 3z + 7 = 7 + 3z. How many solutions does it have?

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Many Solutions

Tags

CCSS.8.EE.C.7A

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

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Simplify both sides of the equation to see if they are equivalent.

Tags

CCSS.8.EE.C.7A

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If you simplify an equation and get a true statement like '0 = 0', what does that indicate?

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It indicates that the equation has 'Many Solutions'.

Tags

CCSS.8.EE.C.7A

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If you simplify an equation and get a false statement like '5 = 3', what does that indicate?

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It indicates that the equation has 'No Solution'.

Tags

CCSS.8.EE.C.7A