Retake PracticeSystems of Linear Inequalities Practical Problems

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What is a linear inequality?

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A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (such as <, >, ≤, or ≥). It represents a region of the coordinate plane.

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What does the symbol '≤' mean in an inequality?

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The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

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What does the symbol '≥' mean in an inequality?

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The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left can be greater than or equal to the value on the right.

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

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What is the feasible region in a system of inequalities?

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The feasible region is the area on a graph where all the inequalities in a system overlap. It represents all possible solutions that satisfy all inequalities.

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What is the difference between 'and' and 'or' in systems of inequalities?

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In systems of inequalities, 'and' means that both conditions must be satisfied simultaneously, while 'or' means that at least one of the conditions must be satisfied.

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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, 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 importance of the boundary line in a linear inequality?

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The boundary line indicates the limit of the solution set. Points on the line may or may not be included in the solution set, depending on whether the inequality is strict (< or >) or inclusive (≤ or ≥).

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What is a practical problem involving linear inequalities?

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A practical problem involving linear inequalities might include scenarios like budgeting, resource allocation, or production limits, where constraints are expressed as inequalities.

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How can you represent a real-world situation with a system of inequalities?

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To represent a real-world situation, identify the variables, constraints, and objectives. Formulate inequalities based on the relationships and limits described in the scenario.