No Solution/Infinite Solution/One Solution

Front

What does it mean if an equation has no solution?

Back

An equation has no solution when there are no values that can satisfy the equation, often resulting in a contradiction.

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What does it mean if an equation has one solution?

Back

An equation has one solution when there is exactly one value that satisfies the equation.

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What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions when any value satisfies the equation, often resulting in an identity.

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Example of an equation with no solution: 2x + 3 = 2x + 5

Back

This equation has no solution because it simplifies to 3 = 5, which is a contradiction.

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Example of an equation with one solution: 3x - 4 = 5

Back

This equation has one solution: x = 3.

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Example of an equation with infinite solutions: 4(x + 1) = 4x + 4

Back

This equation has infinite solutions because it simplifies to 4 = 4, which is always true.

Front

What is the first step in solving linear equations?

Back

The first step is to simplify both sides of the equation, if possible, by combining like terms.

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How do you determine if an equation has infinite solutions?

Back

An equation has infinite solutions if, after simplifying, both sides are identical.

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How do you determine if an equation has no solution?

Back

An equation has no solution if simplifying leads to a false statement, such as 0 = 5.

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What is a linear equation?

Back

A linear equation is an equation that can be written in the form ax + b = c, where a, b, and c are constants.