linear inequalities

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What is a linear inequality?

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

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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 shaded region represent in the graph of a linear inequality?

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The shaded region represents all the possible solutions to the inequality. Points in the shaded area satisfy the inequality.

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What is the difference between a solid line and a dashed line in graphing inequalities?

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A solid line indicates that points on the line are included in the solution (for ≤ or ≥), while a dashed line indicates that points on the line are not included (for < or >).

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Yes, substituting (0, 0) gives 0 + 0 < 7, which is true.

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What does it mean if a point lies on the boundary line of a linear inequality?

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If a point lies on the boundary line, it may or may not be a solution depending on whether the inequality is strict (< or >) or inclusive (≤ or ≥).

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How do you determine if a point is a solution to a linear inequality?

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Substitute the coordinates of the point into the inequality. If the inequality holds true, then the point is a solution.

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What is the significance of the origin (0, 0) in linear inequalities?

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