Solving Inequalities and Absolute Value Equations

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What is an inequality?

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An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, or equal to the other.

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What does it mean to solve an inequality?

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To solve an inequality means to find all values of the variable that make the inequality true.

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What is the solution set of an inequality?

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The solution set of an inequality is the set of all values that satisfy the inequality.

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What is interval notation?

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Interval notation is a way of writing subsets of the real number line using intervals, such as (a, b) or [a, b].

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How do you graph an inequality on a number line?

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To graph an inequality on a number line, use an open circle for < or > and a closed circle for ≤ or ≥, then shade the appropriate region.

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What is an absolute value equation?

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An absolute value equation is an equation that contains an absolute value expression, such as |x| = a.

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How do you solve an absolute value equation?

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

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The first step is to find the critical points by setting the numerator and denominator to zero.

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What is the difference between strict and non-strict inequalities?

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Strict inequalities (<, >) do not include the endpoints, while non-strict inequalities (≤, ≥) do include the endpoints.