Solving Inequalities

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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, greater than or equal to, or 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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How do you represent inequalities on a number line?

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Inequalities are represented on a number line using open or closed circles to indicate whether endpoints are included or excluded, and shading to show the range of solutions.

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What is the difference between < and ≤?

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The symbol < means 'less than' and does not include the endpoint, while ≤ means 'less than or equal to' and includes the endpoint.

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It represents that twenty-two more than four times a number n is less than 82.

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How do you check if a solution is correct for an inequality?

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To check if a solution is correct, substitute the value back into the original inequality and see if the statement holds true.

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What is a compound inequality?

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A compound inequality consists of two or more inequalities joined by 'and' or 'or'.