How Many Solutions?

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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 that can satisfy the equation. For example, m + 1 = m has no solution because it implies 1 = 0.

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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 can satisfy the equation. For example, 12c + 7 = 12c + 7 is true for all values of c.

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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 that satisfies the equation. For example, 12x = 7x has one solution, which is x = 0.

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What is the equation m + 1 = m an example of?

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It is an example of an equation with no solution.

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What is the equation 7a + 8 = 7a + 1 an example of?

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It is an example of an equation with no solution.

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What is the equation 12c + 7 = 12c + 7 an example of?

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It is an example of an equation with infinite solutions.

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What is the equation 12x = 7x an example of?

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It is an example of an equation with one solution.

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What is the equation 9b - 2 = 9b + 2 an example of?

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It is an example of an equation with no solution.

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How can you determine if an equation has no solution?

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If simplifying the equation leads to a false statement (like 1 = 0), it has no solution.

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How can you determine if an equation has infinite solutions?

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If simplifying the equation leads to a true statement (like 0 = 0), it has infinite solutions.