Solving one variable linear equations

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What is a linear equation?

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A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form ax + b = c, where a, b, and c are constants.

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What does it mean for an equation to have no solution?

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An equation has no solution when there are no values for the variable that can satisfy the equation. This often occurs when the equation simplifies to a false statement, such as 0 = 5.

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How do you solve a linear equation with one variable?

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To solve a linear equation with one variable, isolate the variable on one side of the equation using inverse operations (addition, subtraction, multiplication, division) until the variable is alone.

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What is the significance of the equation 2x + 1 = 2x - 1?

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This equation has no solution because when simplified, it leads to the false statement 1 = -1, indicating that there are no values of x that can satisfy the equation.

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What is the first step in solving the equation -4(3w + 4) - 14 = 3(2w - 4) - 9w?

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The first step is to distribute the -4 and 3 across their respective parentheses to simplify the equation.

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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 on one side by itself, allowing you to find its value.

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What is the solution to the equation w = -2?

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The solution indicates that the value of the variable w is -2, which satisfies the equation when substituted back.

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What is the process of checking a solution in a linear equation?

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To check a solution, substitute the value of the variable back into the original equation to see if both sides are equal.

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What is the result of solving the equation 1/2(4x - 8) = 1/4(8x + 12)?

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The result is that there are no solutions, as the equation simplifies to a false statement.

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What is the importance of understanding the concept of 'no solution' in linear equations?

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Understanding 'no solution' helps students recognize when an equation does not have a valid answer, which is crucial for problem-solving.