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 relates a linear expression to a value using inequality symbols (>, <, ≥, ≤).

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What does the solution set of a linear inequality represent?

Back

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

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How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Then, shade the region that satisfies the inequality.

Front

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 the symbol '≥' mean in a linear inequality?

Back

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

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

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The symbol '<' means 'less than', indicating that the value must be strictly less than the specified number.

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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 into the inequality. If the inequality holds true, 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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The solution set of a system of linear inequalities is the region where the shaded areas of all inequalities overlap.

Front

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

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The boundary line separates the solution set from the non-solution set and indicates the values that satisfy the inequality.