Review Linear Inequalities and systems of inequalities

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What is a linear 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 dashed line for < or > and a solid line for ≤ or ≥. Then shade the region that satisfies the inequality.

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

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The solution set of a system of inequalities represents all the points that satisfy all inequalities in the system simultaneously.

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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 in the solution set of an inequality?

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To determine if a point is in the solution set, substitute the point's coordinates into the inequality. If the inequality holds true, the point is in the solution set.

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What is the standard form of a linear inequality?

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How do you write a linear inequality from a word problem?

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Identify the quantities involved, determine the relationship (greater than, less than, etc.), and express it using variables and an inequality symbol.

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It represents a situation where the total revenue from selling x glasses of hot chocolate and y glasses of hot apple cider must be at least $240.

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How can you solve a system of inequalities graphically?

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To solve a system of inequalities graphically, graph each inequality on the same coordinate plane and identify the region where the shaded areas overlap.