TEST: Systems/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 (>, <, ≥, ≤). It represents a region of the coordinate plane.

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How do you solve a linear inequality?

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To solve a linear inequality, isolate the variable on one side of the inequality sign using inverse operations, similar to solving an equation. Remember to reverse the inequality sign when multiplying or dividing by a negative number.

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What does the solution set of an inequality represent?

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The solution set of an inequality represents all the values of the variable that make the inequality true, often depicted as a range on a number line or a shaded region on a graph.

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What is the difference between strict and non-strict inequalities?

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Strict inequalities (<, >) do not include the boundary points, while non-strict inequalities (≤, ≥) include the boundary points in the solution set.

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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 dashed line (for < or >) or a solid line (for ≤ or ≥). Then shade the region that satisfies the inequality.

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

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The boundary line in a linear inequality separates the solution set from the non-solution set. Points on the line are included if the inequality is non-strict (≤ or ≥) and excluded if it is strict (< or >).

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What is a system of linear inequalities?

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A system of linear inequalities consists of two or more linear inequalities that are considered simultaneously. The solution is the region where the shaded areas of all inequalities overlap.

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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 to a system of inequalities, substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

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What is the role of the distributive property in solving inequalities?

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The distributive property allows you to multiply a single term by terms inside parentheses. It is crucial for simplifying expressions in inequalities before isolating the variable.