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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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dotted line (for < or >). Then shade the region that satisfies the inequality.

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

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The symbol '>' means that the values on the left side of the inequality are greater than the values on the right side.

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

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The symbol '<' means that the values on the left side of the inequality are less than the values on the right side.

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

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The symbol '≥' means that the values on the left side of the inequality are greater than or equal to the values on the right side.

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

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The symbol '≤' means that the values on the left side of the inequality are less than or equal to the values on the right side.

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What is the solution set of a linear inequality?

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The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality.

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

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To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

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

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

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What is an example of a linear inequality?

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