Unit 3 Ch. 3 8: Solving Equations

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What is an equation?

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An equation is a mathematical statement that asserts the equality of two expressions, typically containing variables.

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What does it mean to solve an equation?

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To solve an equation means to find the value(s) of the variable(s) that make the equation true.

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What is a solution to an equation?

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A solution to an equation is a value that, when substituted for the variable, makes the equation true.

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What are infinite solutions in an equation?

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Infinite solutions occur when an equation is true for all values of the variable, indicating that the two sides of the equation are equivalent.

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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 are no values for the variable that can satisfy the equation.

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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 and graphs as a straight line.

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How do you isolate a variable in an equation?

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To isolate a variable, you perform inverse operations to get the variable alone on one side of the equation.

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What is the distributive property?

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The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by two or more terms inside a set of parentheses.

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The solution is infinite solutions, as both sides simplify to the same expression.