Multi-Step Equation (includes 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 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 for 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 for the variable that can satisfy the equation, indicating a contradiction.

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How do you solve the equation 2(x+5) = 2x + 5?

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Distributing gives 2x + 10 = 2x + 5. Subtracting 2x from both sides results in 10 = 5, which is a contradiction, indicating 'no solution' (N).

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What is the first step in solving the equation 5(x - 3) + 2x = 41?

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The first step is to distribute 5 to (x - 3), resulting in 5x - 15 + 2x = 41.

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What is the solution to the equation -3x = -3x?

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This equation has infinite solutions (I) because both sides are identical for any value of x.

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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 0 = 5.

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What is the significance of the equation 1x = 1x - 5?

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This equation has no solution (N) because simplifying it leads to 0 = -5, which is a contradiction.

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What is the process of isolating a variable in an equation?

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Isolating a variable involves rearranging the equation to get the variable on one side and the constant on the other, often using inverse operations.

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What does it mean to simplify an equation?

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Simplifying an equation means to combine like terms and reduce the equation to its simplest form.