Writing and Solving Inequalities and Systems of Inequalities

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What is an inequality?

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An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

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What does it mean for a point to be a solution to an inequality?

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A point is a solution to an inequality if it satisfies the inequality when the coordinates of the point are substituted into the inequality.

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What is a system of inequalities?

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A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

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How do you graph an inequality in two variables?

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To graph an inequality, first graph the corresponding equation as a line. Then, use a dashed line for < or > and a solid line for ≤ or ≥. Shade the region that satisfies the inequality.

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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 line, while non-strict inequalities (≤, ≥) include the boundary line.

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

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

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What does the solution set of a system of inequalities represent?

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The solution set represents all the points that satisfy all inequalities in the system, often visualized as a shaded region on a graph.

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How do you solve a system of inequalities algebraically?

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To solve a system of inequalities algebraically, solve each inequality for one variable and then find the intersection of the solution sets.

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What is the significance of the boundary line in an inequality?

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The boundary line indicates the limits of the solution set. Points on the line are included if the inequality is non-strict (≤ or ≥) and excluded if strict (< or >).