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 one or more 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 linear equation?

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A linear equation is an equation of the first degree, meaning it has no variables raised to a power greater than one.

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What are the possible types of solutions for an equation?

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An equation can have one solution, no solution, or infinitely many solutions.

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What does 'one solution' mean in the context of equations?

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'One solution' means there is exactly one value for the variable that satisfies the equation.

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What does 'no solution' mean in the context of equations?

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'No solution' means there is no value for the variable that can satisfy the equation.

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What does 'infinite solutions' mean in the context of equations?

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'Infinite solutions' means that there are countless values for the variable that satisfy the equation, often because the equation is an identity.

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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 both sides of the equation until the variable is alone on one side.

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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 parentheses.

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One Solution.