Types of Solutions

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What is a solution in mathematics?

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A solution is a value or set of values that satisfy an equation.

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What does 'no solution' mean in an equation?

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No matter what constant is substituted in for the variable, the equation will NEVER be true.

Tags

CCSS.8.EE.C.7A

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What does 'one solution' mean in an equation?

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Only this ONE solution will make the equation true.

Tags

CCSS.7.EE.B.4A

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What does 'infinite solutions' mean in an equation?

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There are countless values that can satisfy the equation.

Tags

CCSS.8.EE.C.7A

Front

How do you determine if an equation has no solution?

Back

If the equation simplifies to a false statement, like 0 = 5.

Tags

CCSS.8.EE.C.7A

Front

How do you determine if an equation has one solution?

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If the equation simplifies to a true statement with a specific value for the variable.

Tags

CCSS.8.EE.C.7A

Front

How do you determine if an equation has infinite solutions?

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If the equation simplifies to a true statement that is always valid, like 0 = 0.

Tags

CCSS.8.EE.C.7A

Front

What is the equation for a line with infinite solutions?

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An example is 2x + 3 = 2(x + 1) + 1.

Tags

CCSS.8.EE.C.7A

Front

What is the first step in solving an equation?

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Isolate the variable on one side of the equation.

Tags

CCSS.7.EE.B.4A

Front

What is the importance of checking your solution?

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To ensure that the solution satisfies the original equation.

Tags

CCSS.8.EE.C.7B