Solving Equations: Solution Types

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What is the definition of an equation?

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An equation is a mathematical statement that asserts the equality of two expressions, typically containing one or more variables.

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CCSS.HSA.REI.A.1

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What does it mean for an equation to have one solution?

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An equation has one solution when there is exactly one value of the variable that makes the equation true.

Tags

CCSS.8.EE.C.7A

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What does it mean for an equation to have no solution?

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An equation has no solution when there is no value of the variable that can satisfy the equation.

Tags

CCSS.8.EE.C.7A

Front

What does it mean for an equation to have infinite solutions?

Back

An equation has infinite solutions when any value of the variable satisfies the equation, indicating that the two sides of the equation are equivalent for all values.

Tags

CCSS.8.EE.C.7A

Front

How do you determine if an equation has one solution, no solution, or infinite solutions?

Back

To determine the type of solution, simplify the equation and analyze the resulting expressions. If they are equivalent, there are infinite solutions; if they lead to a contradiction, there is no solution; if they yield a single value, there is one solution.

Tags

CCSS.8.EE.C.7A

Front

What is the first step in solving a linear equation?

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The first step in solving a linear equation is to isolate the variable on one side of the equation.

Tags

CCSS.7.EE.B.4A

Front

What is the significance of the distributive property in solving equations?

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The distributive property allows you to multiply a single term by each term inside a set of parentheses, which is essential for simplifying equations.

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CCSS.6.EE.A.3

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What is a contradiction in the context of equations?

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A contradiction occurs when simplifying an equation leads to a false statement, such as 0 = 5, indicating that there are no solutions.

Tags

CCSS.8.EE.C.7A

Front

What is the role of combining like terms in solving equations?

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Combining like terms helps to simplify the equation, making it easier to isolate the variable and find the solution.

Tags

CCSS.7.EE.B.4A

Front

What is the purpose of checking your solution after solving an equation?

Back

Checking your solution ensures that the value found satisfies the original equation, confirming its correctness.

Tags

CCSS.8.EE.C.7B