Solving Linear Inequalities and Word Problems

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What is a linear inequality?

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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. Remember to reverse the inequality sign when multiplying or dividing by a negative number.

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What does the solution of a linear inequality represent?

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The solution of a linear inequality represents a range of values that satisfy the inequality, often expressed as an interval or a graph on a number line.

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What is the difference between a strict and non-strict inequality?

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A strict inequality uses < or >, meaning the values cannot equal the boundary. A non-strict inequality uses ≤ or ≥, meaning the values can equal the boundary.

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How do you graph a linear inequality on a number line?

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To graph a linear inequality on a number line, use an open circle for strict inequalities (<, >) and a closed circle for non-strict inequalities (≤, ≥). Shade the region that represents the solution.

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What is a word problem in mathematics?

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A word problem is a mathematical question presented in a narrative form, requiring the reader to extract relevant information and formulate a mathematical expression or equation to find a solution.

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How do you approach solving a word problem?

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1. Read the problem carefully. 2. Identify the known and unknown variables. 3. Translate the words into a mathematical equation. 4. Solve the equation. 5. Interpret the solution in the context of the problem.

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What is the importance of checking your solution in inequalities?

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Checking your solution ensures that the values satisfy the original inequality. It helps confirm that the solution is correct and that no mistakes were made during the solving process.