No Solution, One Solution, Infinite Solutions

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What does it mean if an equation has Infinite Solutions?

Back

An equation has Infinite Solutions when every value of the variable satisfies the equation, meaning the two sides of the equation are identical for all values.

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, indicating a contradiction.

Tags

CCSS.8.EE.C.7A

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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 of the variable that satisfies the equation.

Tags

CCSS.8.EE.C.7A

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Solve the equation: 12(y+2)=6(2y+4)

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Infinite Solutions

Tags

CCSS.8.EE.C.7A

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Solve the equation: -10y-6 = -10y-6

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Infinite Solutions

Tags

CCSS.8.EE.C.7A

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Solve the equation: 8m+12=2(4m+6)

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Infinite Solutions

Tags

CCSS.8.EE.C.7A

Front

Solve the equation: 9y+8=9y-8

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No Solution

Tags

CCSS.8.EE.C.7A

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Solve the equation: 2(m+3)=2m+12

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No Solution

Tags

CCSS.8.EE.C.7A

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What is an example of an equation with Infinite Solutions?

Back

An example is 2x + 4 = 2(x + 2). Both sides simplify to the same expression.

Tags

CCSS.8.EE.C.7A

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What is an example of an equation with No Solution?

Back

An example is 3x + 5 = 3x - 2. This leads to a contradiction (5 = -2).

Tags

CCSS.8.EE.C.7A