Solving Equations: Special Cases

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What is 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 if an equation has no solution?

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An equation has no solution when there are no values for the variable that can satisfy the equation, often resulting in a false statement like 4=5.

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What does it mean if an equation has infinitely many solutions?

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An equation has infinitely many solutions when any value of the variable satisfies the equation, often resulting in a true statement like 0=0.

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How do you determine if an equation has one solution?

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An equation has one solution if there is exactly one value for the variable that makes the equation true.

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Infinitely many solutions.

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Infinitely many solutions.

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One solution: x = 4.

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One solution: x = \frac{1}{2}.

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What does it mean if an equation simplifies to a false statement?

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If an equation simplifies to a false statement, it indicates that there are no solutions.

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What is the first step in solving an equation?

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The first step is to simplify both sides of the equation, if possible, by combining like terms.