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.

Tags

CCSS.8.EE.C.7A

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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.

Tags

CCSS.8.EE.C.7A

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

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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.

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Example of an equation with many solutions:

Back

8y - 4 = 8y - 4.

Tags

CCSS.8.EE.C.7A

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Example of an equation with no solution:

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4y + 5 = 4y - 7.

Tags

CCSS.8.EE.C.7A

Front

Example of an equation with one solution:

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x - 3 = 2.

Tags

CCSS.6.EE.B.7

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

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

Tags

CCSS.8.EE.C.7A

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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.

Tags

CCSS.8.EE.C.7A

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How can you identify an equation with many solutions?

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

Tags

CCSS.8.EE.C.7A

Front

How can you identify an equation with no solution?

Back

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

Tags

CCSS.8.EE.C.7A