Linear inequalities (one variable)

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What is a linear inequality?

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A linear inequality is a mathematical expression that shows the relationship between two expressions using inequality symbols (like <, >, ≤, or ≥) instead of an equal sign.

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What does the symbol '≤' mean in a linear inequality?

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The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

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What does the symbol '≥' mean in a linear inequality?

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The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left can be greater than or equal to the value on the right.

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When graphing a linear inequality with '≤' or '≥', what type of line is used?

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A solid line is used when graphing a linear inequality with '≤' or '≥' to indicate that points on the line are included in the solution.

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When graphing a linear inequality with '<' or '>', what type of line is used?

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A dashed line is used when graphing a linear inequality with '<' or '>' to indicate that points on the line are not included in the solution.

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What does it mean if a solution to a linear inequality is represented on a number line?

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It means that all the values in the solution set are included in the shaded region of the number line, indicating which values satisfy the inequality.