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 solutions on a graph.

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What does the symbol '≤' mean in a linear 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.

Front

What does the symbol '≥' mean in a linear inequality?

Back

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.

Front

How do you graph a linear inequality?

Back

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 the context of linear inequalities?

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The feasible region is the area on a graph where all the constraints (linear inequalities) overlap. It represents all possible solutions to the system of inequalities.

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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 in the solution set.

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In the context of a problem, what does 'at least' indicate when forming inequalities?

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'At least' indicates a minimum value and is represented by a 'greater than or equal to' (≥) inequality.

Front

In the context of a problem, what does 'no more than' indicate when forming inequalities?

Back

'No more than' indicates a maximum value and is represented by a 'less than or equal to' (≤) inequality.

Front

If x represents the number of 2-point shots and y represents the number of 3-point shots, how would you express scoring at least 20 points?

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Front

If x represents the number of hours worked at a job earning $9/hour and y represents hours at a job earning $25/hour, how would you express earning at least $200?

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