Solving Equations with Variables on Both Sides

Front

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.

Front

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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Back

x = 5

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Back

x = 3

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Back

x = 6

Front

Back

x = 6

Front

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.

Front

What does it mean if an equation has many solutions?

Back

It means that any value for the variable will satisfy the equation, often resulting in a true statement like 0 = 0.

Front

What is the importance of isolating the variable in an equation?

Back

Isolating the variable allows us to find its value, which is the solution to the equation.