Solving Equations with Variables on Both Sides

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What does it mean to have variables on both sides of an equation?

Back

It means that the variable (e.g., x) appears on both sides of the equation, requiring manipulation to isolate the variable.

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What is the first step in solving an equation with variables on both sides?

Back

The first step is to get all terms containing the variable on one side of the equation and constant terms on the other side.

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Back

No solution.

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What does it mean if an equation has no solution?

Back

It means that there are no values for the variable that can satisfy the equation.

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Back

x = 6.

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What is the significance of the distributive property in solving equations?

Back

The distributive property allows you to multiply a single term by terms inside parentheses, which is essential for simplifying equations.

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All real numbers.

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

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

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x = -11.

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What is the goal when solving an equation?

Back

The goal is to isolate the variable on one side of the equation to find its value.