Linear Inequalities and 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 (>, <, ≥, ≤).

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What does the solution set of a linear inequality represent?

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The solution set of a linear inequality represents all the possible values (points) 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 satisfies the inequality (above or below the line).

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What is a system of linear inequalities?

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A system of linear inequalities is a set 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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The solution set of a system of linear inequalities is the region where the shaded areas of all inequalities overlap.

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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 equal to the boundary line.

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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 equal to the boundary line.

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What is the significance of the boundary line in a linear inequality?

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The boundary line represents the values that make the inequality an equation. Points on the line are included if the inequality is '≤' or '≥'.

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How do you determine if a point is part of the solution set for a linear inequality?

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To determine if a point is part of the solution set, substitute the point's coordinates into the inequality. If the inequality holds true, the point is part of the solution set.

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What is the first step in writing a system of inequalities from a word problem?

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Identify the variables and the constraints described in the problem.