Linear Inequalities and Systems of Linear Inequalities

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What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

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

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The symbol '≥' means 'greater than or equal to', indicating that the value can be either greater than or equal to a specified number.

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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', indicating that the value can be either less than or equal to a specified number.

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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 values that satisfy the inequality.

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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. Then, shade the region that represents the solution set based on the inequality symbol.

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What is the difference between a solid line and a dashed line in graphing inequalities?

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A solid line indicates that points on the line are included in the solution set (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

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What does it mean if a point lies on the boundary line of a linear inequality?

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If a point lies on the boundary line, it is part of the solution set if the line is solid (≥ or ≤) and not part of the solution set if the line is dashed (> or <).

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

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To determine if a point is a solution, substitute the coordinates of the point 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.

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How do you find the solution set of a system of linear inequalities?

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To find the solution set, graph each inequality on the same coordinate plane and identify the region where the shaded areas overlap.