Number of Solutions

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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 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.

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What does it mean if an equation has one solution?

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An equation has one solution when there is exactly one value for the variable that satisfies the equation.

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What does it mean if an equation has infinite solutions?

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An equation has infinite solutions when any value for the variable satisfies the equation, often occurring when both sides of the equation are identical.

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This equation simplifies to 1 = 1, which is always true, indicating it has infinite solutions.

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This equation simplifies to 50x = -10, leading to one solution: x = -1/5.

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This equation simplifies to 25 = 25, which is always true, indicating it has infinite solutions.

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Subtract 12 from both sides to find x = 8.

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This equation simplifies to 10x = -25, leading to one solution: x = -2.5.

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What is a variable in an equation?

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A variable is a symbol, often represented by a letter, that stands for an unknown value in an equation.