Solutions to Linear Inequalities Flashcard

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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 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.

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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 boundary line. Use a solid line for ≤ or ≥ and a dashed line for < or >. Then shade the region that satisfies the inequality.

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What does it mean if a point is in the shaded region of a graph of a linear inequality?

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If a point is in the shaded region, it means that the point satisfies the inequality.

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

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If a point is on the boundary line, whether it is included in the solution set depends on whether the line is solid (included) or dashed (not included).

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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, the point is a solution.

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What is the difference between a solid line and a dashed line in the graph of a linear inequality?

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

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What is the significance of the inequality symbol in a linear inequality?

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The inequality symbol indicates the relationship between the two expressions and determines the direction of the shading in the graph.

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Substitute the x and y values of the point into the inequality. If the resulting statement is true, then the point is a solution.

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Substituting (1, 4) gives 4 < 2(1) + 3, which simplifies to 4 < 5. This is true, so (1, 4) is a solution.