Systems of Inequalities Word Problems

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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 that share 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 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 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 is either greater 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 'less than or equal to'. It indicates that the value on the left is either less than or equal to the value on the right.

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How can 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 significance of the feasible region in a system of inequalities?

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The feasible region is the area on the graph where all the inequalities overlap. It represents all possible solutions to the system.

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What is the first step in solving a word problem involving a system of inequalities?

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The first step is to define the variables that represent the quantities in the problem.

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What is an example of a real-world application of systems of inequalities?

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An example is budgeting, where you might have constraints on spending and income, leading to a system of inequalities to represent the situation.

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What does it mean for a solution to be 'bounded' in a system of inequalities?

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A bounded solution means that the feasible region is enclosed, having a maximum and minimum value, unlike unbounded solutions that extend infinitely.

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How do you write an inequality from a word problem?

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Identify the key quantities and relationships in the problem, then translate them into an inequality using appropriate symbols.