One Solution, No Solution, Many Solutions

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What does it mean if an equation has 'No Solution'?

Back

An equation has 'No Solution' when there are no values that can satisfy the equation. This often occurs when simplifying leads to a contradiction, such as 0 = 5.

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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, the equation 2x = 8 has one solution: x = 4.

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What does it mean if an equation has 'Many Solutions'?

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An equation has 'Many Solutions' when any value can satisfy the equation. This typically occurs when both sides of the equation are identical, such as x = x.

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Solve the equation: 4y + 5 = 4y - 7

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No Solution

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Solve the equation: 3x = x + 4

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One Solution: x = 2

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Solve the equation: 3z + 8 = 2 + 3z

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No Solution

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Solve the equation: Z = Z

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Many Solutions

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What is an example of an equation with 'No Solution'?

Back

An example is 2x + 3 = 2x - 5, which simplifies to 3 = -5.

Front

What is an example of an equation with 'One Solution'?

Back

An example is x + 2 = 5, which has the solution x = 3.

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What is an example of an equation with 'Many Solutions'?

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An example is 5(x + 1) = 5x + 5, which simplifies to 5 = 5.