No Solution, One Solution, Infinite Solutions

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What does it mean when an equation has infinite solutions?

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An equation has infinite solutions when both sides of the equation are identical, meaning any value for the variable will satisfy the equation.

Tags

CCSS.8.EE.C.7A

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What is an example of an equation with infinite solutions?

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An example is -10y - 6 = -10y - 6, where both sides are the same.

Tags

CCSS.8.EE.C.7A

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What does it mean when an equation has no solution?

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An equation has no solution when it leads to a contradiction, meaning there is no value for the variable that can satisfy the equation.

Tags

CCSS.8.EE.C.7A

Front

What is an example of an equation with no solution?

Back

An example is 2(m + 3) = 2m + 12, which simplifies to a false statement.

Tags

CCSS.8.EE.C.7A

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What does it mean when an equation has one solution?

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

Tags

CCSS.8.EE.C.7A

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What is an example of an equation with one solution?

Back

An example is 6(m + 3) = 5(m - 2), which simplifies to a single value for m.

Tags

CCSS.8.EE.C.7A

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How can you determine if an equation has infinite solutions, no solution, or one solution?

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You can determine this by simplifying the equation and analyzing the resulting statements. If both sides are identical, it has infinite solutions; if it leads to a contradiction, it has no solution; if it simplifies to a single value, it has one solution.

Tags

CCSS.8.EE.C.7A

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What is the significance of the coefficients in determining the number of solutions?

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The coefficients of the variables in an equation help determine the relationship between the variables. If they are proportional in a way that leads to a contradiction, there is no solution; if they are identical, there are infinite solutions.

Tags

CCSS.8.EE.C.8B

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What is the first step in solving an equation to find its solutions?

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The first step is to simplify both sides of the equation as much as possible, combining like terms and isolating the variable.

Tags

CCSS.8.EE.C.7B

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What is a contradiction in the context of equations?

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A contradiction occurs when an equation simplifies to a statement that is always false, such as 0 = 5.

Tags

CCSS.8.EE.C.7A