Equations with One, Infinite, or No Solutions

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What is an equation with no solution?

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An equation with no solution is one that cannot be satisfied by any value of the variable. This occurs when the two sides of the equation represent parallel lines that never intersect.

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What is an equation with infinitely many solutions?

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An equation with infinitely many solutions is one where any value of the variable satisfies the equation. This typically happens when both sides of the equation are equivalent expressions.

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no solution

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no solution

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infinitely many solutions

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infinitely many solutions

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What does it mean if an equation has one solution?

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An equation with one solution has exactly one value for the variable that makes the equation true. This occurs when the two sides of the equation intersect at a single point.

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What is the first step in solving a linear equation?

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The first step is to simplify both sides of the equation, which may involve distributing, combining like terms, or moving terms from one side to the other.

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What is the significance of the variable in an equation?

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The variable represents an unknown value that we are trying to solve for. It is essential in forming equations and finding solutions.