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What is a linear inequality?

Back

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

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What does the solution set of a linear inequality represent?

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The solution set of a linear inequality represents all the points (x, y) that satisfy the inequality, often visualized as a region on a graph.

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

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

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How do 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 part of the solution set.

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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 may or may not be included in the solution set, depending on whether the line is solid or dotted.

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What is the significance of the boundary line in a linear inequality?

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The boundary line separates the solution set from the non-solution set in the graph of a linear inequality.

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How can you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a line, then shade the appropriate region based on the inequality symbol.

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What is the role of test points in solving linear inequalities?

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Test points are used to determine which side of the boundary line is part of the solution set by substituting the test point into the inequality.

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What is the solution to the inequality y > 2x + 1?

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The solution includes all points above the line y = 2x + 1, not including the line itself.

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What does it mean for a point to be 'not part of the solution set'?

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A point is 'not part of the solution set' if it does not satisfy the inequality when its coordinates are substituted into the inequality.