Solving Equations Review

Front

What is the definition of an absolute value equation?

Back

An absolute value equation is an equation that contains an absolute value expression, which represents the distance of a number from zero on the number line.

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How do you solve an absolute value equation?

Back

To solve an absolute value equation, you set up two separate equations: one for the positive case and one for the negative case, then solve each equation.

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What is set notation?

Back

Set notation is a mathematical notation used to describe a set of numbers, typically represented with curly braces, e.g., {x | condition}.

Front

What is the process for solving exponential equations?

Back

To solve exponential equations, you can use properties of exponents to rewrite the equation in a form that allows you to equate the exponents or take logarithms.

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What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain a given number, commonly denoted as log_b(a) where b is the base and a is the result.

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How do you isolate a variable in a rational equation?

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To isolate a variable in a rational equation, you can cross-multiply if the equation is in the form of a fraction, then solve for the variable.

Front

What is the square root property?

Back

The square root property states that if x^2 = a, then x = ±√a, allowing you to solve equations involving squares.

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What are the steps to check if a solution is valid in an equation?

Back

To check if a solution is valid, substitute the solution back into the original equation and verify if both sides are equal.

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What is the significance of extraneous solutions?

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Extraneous solutions are solutions that emerge from the solving process but do not satisfy the original equation; they must be checked and discarded.

Front

How do you solve a radical equation?

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To solve a radical equation, isolate the radical on one side, then square both sides to eliminate the radical, and solve the resulting equation.