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, while remembering to reverse the inequality sign if you multiply or divide 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 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, draw a number line, use an open circle for strict inequalities (< or >) and a closed circle for non-strict inequalities (≤ or ≥), then shade the region that represents the solution.

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What does it mean to isolate the variable in an inequality?

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Isolating the variable means rearranging the inequality so that the variable is on one side and all other terms are on the opposite side.

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What is a word problem in the context of linear inequalities?

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A word problem is a real-life scenario that can be modeled using linear inequalities, requiring the formulation of an inequality based on the given information.

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How can you check your solution to a linear inequality?

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You can check your solution by substituting a value from the solution set back into the original inequality to see if it holds true.