How Many Solutions Multi-Step Equations

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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 if an equation has infinite solutions?

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An equation has infinite solutions when any value for the variable makes the equation true, indicating that the two sides of the equation are equivalent.

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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 is no value for the variable that can make the equation true, indicating a contradiction.

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What is the first step in solving a multi-step equation?

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The first step is often to simplify both sides of the equation by combining like terms or distributing.

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How do you determine if an equation has one solution?

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An equation has one solution if, after simplifying, you can isolate the variable to find a specific value that satisfies the equation.

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Solve the equation: 2z - 6 = 2(z + 2) - 10

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Infinite solutions.

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Solve the equation: 5x + 6 = 2 + 3x

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One solution: x = 1.

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Solve the equation: 2x + 1 = 2x - 1

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No solution.

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What is the significance of combining like terms in an equation?

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Combining like terms helps to simplify the equation, making it easier to solve.

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What is the distributive property?

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The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by each term inside a parenthesis.