Solving Equations

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What is the general form of a linear equation?

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How do you isolate a variable in an equation?

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To isolate a variable, perform inverse operations to both sides of the equation until the variable is alone on one side.

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What does it mean if an equation has no solution?

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An equation has no solution if there are no values for the variable that can satisfy the equation, often resulting in a contradiction.

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What does it mean if an equation has infinite solutions?

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An equation has infinite solutions if any value for the variable satisfies the equation, often resulting in a tautology.

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Combine like terms to find that there are no solutions.

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This equation has infinite solutions because both sides are identical.

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What is the purpose of checking your solution in an equation?

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Checking your solution verifies that the value satisfies the original equation.