(CORE) Solving Multi-Step Equations_Special Cases

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What is a multi-step equation?

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A multi-step equation is an equation that requires more than one step to solve, often involving operations like addition, subtraction, multiplication, and division.

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What does it mean for an equation to have no solution?

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An equation has no solution when there are no values that can satisfy the equation, often resulting in a contradiction.

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What does it mean for an equation to have infinitely many solutions?

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

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What is the significance of the equation x + 10 = x + 1?

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This equation has no solution because simplifying it leads to a contradiction (10 = 1).

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What is the significance of the equation 5(2x + 3) = 15 + 10x?

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This equation has infinitely many solutions because both sides simplify to the same expression.

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What does the equation x = -24 indicate?

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This equation indicates that there is one specific solution for x, which is -24.

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What does the equation -24 = -24 indicate?

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This equation indicates that there are infinitely many solutions, as it is always true.

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What does the equation -24 = -36 indicate?

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This equation indicates that there is no solution, as it presents a contradiction.

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How do you determine if an equation has no solution?

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An equation has no solution if simplifying it leads to a false statement, such as 5 = 3.

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How do you determine if an equation has infinitely many solutions?

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An equation has infinitely many solutions if simplifying it leads to a true statement, such as 0 = 0.