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 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 endpoints are not included. A non-strict inequality uses ≤ or ≥, meaning the endpoints are included.

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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 appropriate side.

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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 compound inequality?

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How do you solve a compound inequality?

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To solve a compound inequality, solve each inequality separately and then find the intersection (for 'and') or the union (for 'or') of the solutions.