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?

Back

The symbol '≤' means 'less than or equal to', indicating 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 a linear inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating 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?

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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 is the solution set of a linear inequality?

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The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality.

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

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What does it mean if a point is a solution to a system of linear inequalities?

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A point is a solution to a system of linear inequalities if it satisfies all the inequalities in the system.

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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 where the inequality changes from true to false. Points on the line are included if the inequality is ≤ 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 x and y values of the point into the inequality and check if the statement is true.