Multi-Step Equation: One/No/Infinite Solutions

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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 such as 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 of the variable satisfies the equation, indicating that the two sides of the equation are equivalent for all values.

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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 of the variable that can satisfy the equation, indicating a contradiction.

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How do you determine if a multi-step equation has one solution, no solution, or infinite solutions?

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To determine the type of solution, simplify the equation step by step. If you end up with a true statement (like 0=0), it has infinite solutions. If you get a false statement (like 0=5), it has no solution. If you find a specific value for the variable, it has one solution.

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What is the first step in solving the equation 4 - 6x - 2 = -2(3x - 1)?

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

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What is the solution to the equation 7(4x + 7) = 8x - 31?

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The solution is x = -4.

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What is the solution to the equation 5(x - 3) + 2x = 41?

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The solution is x = 8.

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What does the equation 1x = 1x - 5 imply?

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This equation implies that there is no solution, as it simplifies to a false statement.

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What is the solution to the equation 3x + 5(-7x + 1) = -91?

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The solution is x = 3.

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What is the importance of combining like terms in multi-step equations?

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Combining like terms simplifies the equation, making it easier to isolate the variable and solve.