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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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.

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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.

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

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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.

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

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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.

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.

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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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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.

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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.

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

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