Solving Equations with No Solution and Infinite Solutions

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What is an equation with no solution?

Back

An equation with no solution is one that cannot be satisfied by any value of the variable. This typically occurs when the variable terms cancel out, leaving a false statement (e.g., 0 = 5).

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What is an equation with infinitely many solutions?

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An equation with infinitely many solutions is one that is true for all values of the variable. This occurs when the variable terms cancel out, leaving a true statement (e.g., 0 = 0).

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How do you determine if an equation has no solution?

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To determine if an equation has no solution, simplify the equation and check if it leads to a contradiction, such as a false statement like 0 = 5.

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How do you determine if an equation has infinitely many solutions?

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To determine if an equation has infinitely many solutions, simplify the equation and check if it leads to a true statement, such as 0 = 0.

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What is the first step in solving a linear equation?

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The first step in solving a linear equation is to isolate the variable on one side of the equation by performing inverse operations.

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What does it mean to isolate a variable in an equation?

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Isolating a variable means rearranging the equation so that the variable is alone on one side, making it easier to solve for its value.

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What is the significance of the distributive property in solving equations?

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The distributive property allows you to multiply a single term by terms inside parentheses, which is essential for simplifying equations.

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What is the solution to the equation 5x - 14 = 8x + 4?

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The solution to the equation 5x - 14 = 8x + 4 is x = -6.

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What is the solution to the equation 2x + 1 = 2x - 1?

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The equation 2x + 1 = 2x - 1 has no solution, as it simplifies to a false statement.

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What is the solution to the equation 3x + 15 = 3(x + 5)?

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The equation 3x + 15 = 3(x + 5) has infinitely many solutions, as it simplifies to a true statement.