Unit 4 Test Review

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

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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 or solid line, depending on whether the inequality is strict (dashed) or inclusive (solid). Then, shade the region that satisfies the inequality.

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What does it mean for a system of inequalities to have no solution?

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A system of inequalities has no solution when there is no overlapping region that satisfies all inequalities simultaneously, often represented by non-intersecting lines.

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What is the significance of the double shaded area in a system of inequalities?

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The double shaded area indicates the solution set where all inequalities in the system are satisfied simultaneously.

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How do you determine the feasible region in a linear programming problem?

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The feasible region is determined by graphing all constraints (inequalities) and identifying the area where all shaded regions overlap.

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What is the standard form of a linear inequality?

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Front

What does the slope-intercept form of a linear equation look like?

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How can you convert a linear equation to an inequality?

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To convert a linear equation to an inequality, replace the equality sign (=) with an inequality symbol (>, <, ≥, ≤) based on the context of the problem.

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What is the meaning of the budget constraint in a word problem?

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The budget constraint represents the limit on spending, expressed as an inequality that combines the costs of different items within a specified budget.

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How do you interpret the solution to a linear inequality in a real-world context?

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The solution to a linear inequality represents all possible combinations of variables that satisfy the given conditions, often related to constraints like budget or resources.