cfu_Writing & Solving Systems of Linear Inequalities

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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 (>, <, ≥, ≤). It represents a region of solutions on a graph.

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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 symbol '≤' mean in an inequality?

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'≤' 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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'≥' 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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Write an inequality for the situation: A store sells pencils for $0.50 each and erasers for $1.00 each. If you want to spend no more than $10, what is the inequality?

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What is the solution set of a linear inequality?

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The solution set of a linear inequality is the set of all ordered pairs (x, y) that make the inequality true, represented as a shaded region on a graph.

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How do you determine if a point is a solution to a linear inequality?

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To determine if a point (x, y) is a solution, substitute the x and y values into the inequality. If the inequality holds true, then the point is a solution.

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What is a system of linear inequalities?

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A system of linear inequalities consists of two or more linear inequalities that are considered together. The solution is the region where all inequalities overlap.

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Write a system of inequalities for the following situation: You can work a maximum of 20 hours a week at two jobs, and you need to earn at least $200. If job A pays $10/hour and job B pays $15/hour.

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What is the feasible region in a system of linear inequalities?

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