One solution, many solution, no solution

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

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An equation has many solutions when it is true for all values of the variable. For example, the equation 2x + 3 = 2x + 3 is true for any value of x.

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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 of the variable that can make the equation true. For example, the equation 2x + 3 = 2x + 5 is never true.

Front

What does it mean if an equation has 'one solution'?

Back

An equation has one solution when there is exactly one value of the variable that makes the equation true. For example, the equation x + 2 = 5 has one solution: x = 3.

Front

Example of an equation with many solutions:

Back

8y - 4 = 8y - 4.

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Example of an equation with no solution:

Back

4y + 5 = 4y - 7.

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Example of an equation with one solution:

Back

x - 3 = 2.

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What is the general form of an equation with many solutions?

Back

An equation where both sides are identical, such as a = a.

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What is the general form of an equation with no solution?

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An equation where the variable terms cancel out and result in a false statement, such as 0 = 5.

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How can you identify an equation with many solutions?

Back

If simplifying the equation leads to a true statement like 0 = 0.

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How can you identify an equation with no solution?

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If simplifying the equation leads to a false statement like 0 = 5.