Linear Inequalities and Systems of Linear Inequalities

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What are linear inequalities?

Back

Linear inequalities are mathematical expressions that show the relationship between two variables using inequality signs (>, <, ≥, ≤) instead of an equal sign.

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What is the solution set of a linear inequality?

Back

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

Tags

CCSS.HSA.REI.D.12

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Are the points on the boundary line part of the solution set for a linear inequality?

Back

Yes, they are part of the solution set if the inequality is inclusive (≥ or ≤).

Tags

CCSS.HSA.REI.D.12

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the points that satisfy the inequality, typically shaded on one side of the boundary line.

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 x and y values into the inequality and check if the statement is true.

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What is the difference between strict and non-strict inequalities?

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Strict inequalities (<, >) do not include the boundary line, while non-strict inequalities (≤, ≥) do include the boundary line.

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 is a set of two or more linear inequalities with the same variables.

Tags

CCSS.8.EE.C.8B

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How do you graph a system of linear inequalities?

Back

To graph a system of linear inequalities, graph each inequality on the same coordinate plane and identify the region where all inequalities overlap.

Tags

CCSS.HSA.REI.D.12

Front

What does it mean if a point lies in the shaded region of a graph of a linear inequality?

Back

If a point lies in the shaded region, it means that the point is a solution to the inequality.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

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

Tags

CCSS.HSA.REI.D.12