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

Tags

CCSS.7.EE.B.4B

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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 on the left is either greater than or equal to the value on the right.

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 'less than or equal to', indicating that the value on the left is either less than or equal to the value on the right.

Tags

CCSS.6.EE.B.8

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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 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. The solution is the region where the shaded areas of all inequalities overlap.

Tags

CCSS.HSA.REI.D.12

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How can you determine if a point is a solution to a system of inequalities?

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To determine if a point is a solution, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

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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 of a linear inequality, it is a solution if the inequality includes equality (≥ or ≤). If the inequality is strict (> or <), it is not a solution.

Tags

CCSS.HSA.REI.D.12

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What is the solution set of a system of linear inequalities?

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

Tags

CCSS.HSA.REI.D.12

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What is the significance of the slope in a linear inequality?

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The slope indicates the steepness of the line and the direction of the inequality. A positive slope means the line rises, while a negative slope means it falls.

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How do you identify the feasible region in a system of linear inequalities?

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The feasible region is identified by graphing all inequalities and finding the overlapping shaded area that satisfies all conditions.

Tags

CCSS.HSA.REI.D.12