Linear Inequalities

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What is a linear inequality?

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A linear inequality is a mathematical statement that compares 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 'greater than or equal to', indicating that the value on the left is either greater 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 'less than or equal to', indicating that the value on the left is either less than or equal to the value on the right.

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How do you represent a solution to a linear inequality graphically?

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A solution to a linear inequality is represented graphically by shading the region of the graph that satisfies the inequality.

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What type of line is used when graphing inequalities with '≤' or '≥'?

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

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What type of line is used when graphing inequalities with '<' or '>'?

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A dotted line is used when graphing inequalities with '<' or '>' to indicate that points on the line are not included in the solution.

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How do you determine if a point is a solution to a system of inequalities?

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To determine if a point is a solution, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

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Front

What is the difference between a linear equation and a linear inequality?

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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 of a linear inequality, it is included in the solution if the inequality is '≤' or '≥', but not if it is '<' or '>'.