Solving 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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How do you determine the number of solutions for a linear equation?

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The number of solutions for a linear equation can be determined by simplifying the equation. If you end up with a true statement (like 0 = 0), there are infinitely many solutions. If you get a false statement (like 0 = 5), there is no solution. If you get a specific value for the variable, there is one solution.

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What is the first step in solving the equation 7x – 4 + x = -1 + 13x + 7?

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The first step is to combine like terms on both sides of the equation.

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What does it mean if an equation has no solution?

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An equation has no solution if the two sides of the equation are never equal, which typically occurs when simplifying leads to a contradiction.

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What is the process of isolating a variable in an equation?

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Isolating a variable involves rearranging the equation to get the variable on one side and the constants on the other side, often by using inverse operations.

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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 each term inside a set of parentheses, which is essential for simplifying equations.

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How do you simplify the expression -a + 4 + 5a - a - 6?

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Combine like terms: -a + 5a - a = 3a and 4 - 6 = -2, resulting in 3a - 2.

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What is the solution to the equation 2(9x – 6) = 6(3x – 2) + 2?

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This equation has no solution, as both sides simplify to a contradiction.

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What is the importance of checking your solution in an equation?

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Checking your solution ensures that the value satisfies the original equation, confirming that it is correct.

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What are like terms in an algebraic expression?

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Like terms are terms that have the same variable raised to the same power, allowing them to be combined through addition or subtraction.