Solving Multi-Step Equations (with Distributive Property)

Front

What is a multi-step equation?

Back

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

Front

What is the Distributive Property?

Back

The Distributive Property states that a(b + c) = ab + ac, meaning you can distribute a factor across a sum.

Front

How do you solve the equation 2x + 1 = 5x - 3?

Back

Subtract 2x from both sides: 1 = 3x - 3. Then add 3 to both sides: 4 = 3x. Finally, divide by 3: x = 4/3.

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What does it mean if an equation has no solution?

Back

An equation has no solution if there are no values for the variable that make the equation true, often resulting in a contradiction.

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What is the solution to the equation 3(2x + 1) = 6x + 1?

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The equation simplifies to 6x + 3 = 6x + 1, which leads to 3 = 1, a contradiction, indicating no solution.

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How do you apply the Distributive Property to 6(-6 - 5v)?

Back

Distributing gives -36 - 30v.

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What is the first step to solve 2 + 14a = -8 + 9a?

Back

Subtract 9a from both sides: 2 + 5a = -8.

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What is the solution to the equation 4 - 2(x - 3) = 24?

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First, distribute: 4 - 2x + 6 = 24. Combine like terms: 10 - 2x = 24. Then, solve for x: x = -7.

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What does it mean if an equation has infinitely many solutions?

Back

It means that any value for the variable will satisfy the equation, often resulting from equivalent expressions.

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How do you isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations to get the variable alone on one side of the equation.