Solving Linear Inequalities Test Review

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What is a linear inequality?

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A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

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How do you solve a linear inequality?

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To solve a linear inequality, isolate the variable on one side of the inequality using inverse operations, similar to solving an equation, while remembering to reverse the inequality sign if you multiply or divide by a negative number.

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What does the solution set of a linear inequality represent?

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The solution set of a linear inequality represents all the values of the variable that make the inequality true, often depicted on a number line.

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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. It uses parentheses ( ) for open intervals and brackets [ ] for closed intervals.

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In interval notation, the solution is expressed as (3, ∞).

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What is a compound inequality?

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A compound inequality combines two or more inequalities, often connected by 'and' or 'or', indicating the range of values that satisfy all inequalities.

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What is the difference between 'and' and 'or' in compound inequalities?

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'And' means both conditions must be true simultaneously, while 'or' means at least one of the conditions must be true.

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How do you graph the solution of a linear inequality?

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To graph the solution of a linear inequality, draw a number line, use an open circle for < or > and a closed circle for ≤ or ≥, and shade the region that represents the solution set.

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