Linear Inequalities & System of 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 the coordinate plane.

Tags

CCSS.HSA.REI.D.12

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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'. It indicates that the values of the variable can be less than or equal to a certain number.

Tags

CCSS.6.EE.B.8

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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'. It indicates that the values of the variable can be greater than or equal to a certain number.

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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 solid line (for ≥ or ≤) or a dashed line (for > or <). Then shade the region that satisfies the inequality.

Tags

CCSS.HSA.REI.D.12

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

Tags

CCSS.HSA.REI.D.12

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What is a system of inequalities?

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A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the shaded areas of all inequalities overlap.

Tags

CCSS.HSA.REI.D.12

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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 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 does it mean if a region is shaded above a line in a graph of an inequality?

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If a region is shaded above a line, it means that the solutions to the inequality are greater than the line's equation (y > mx + b).

Tags

CCSS.HSA.REI.D.12

Front

What does it mean if a region is shaded below a line in a graph of an inequality?

Back

If a region is shaded below a line, it means that the solutions to the inequality are less than the line's equation (y < mx + b).

Tags

CCSS.HSA.REI.D.12

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What is the solution set of a system of inequalities?

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The solution set of a system of inequalities is the set of all points that satisfy all inequalities in the system, represented by the overlapping shaded region on the graph.

Tags

CCSS.HSA.REI.D.12