Linear Inequalities & Systems of 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 (>, <, ≥, ≤) instead of an equal sign.

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What does the graph of a linear inequality represent?

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

Tags

CCSS.HSA.REI.D.12

Front

How do you graph a linear inequality?

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1. Graph the corresponding linear equation as a dashed or solid line. 2. Choose a test point not on the line to determine which side to shade.

Tags

CCSS.HSA.REI.D.12

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

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

Front

What is a system of inequalities?

Back

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

Tags

CCSS.HSA.REI.D.12

Front

How do you find a solution to a system of inequalities?

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To find a solution, graph each inequality on the same coordinate plane and identify the overlapping shaded region, which represents all possible solutions.

Tags

CCSS.HSA.REI.D.12

Front

What is a feasible region in the context of linear inequalities?

Back

The feasible region is the area on the graph where all the inequalities in a system are satisfied, representing all possible solutions.

Tags

CCSS.HSA.REI.D.12

Front

What does it mean for a point to be a solution to a system of inequalities?

Back

A point is a solution to a system of inequalities if it lies within the feasible region, meaning it satisfies all inequalities in the system.

Tags

CCSS.HSA.REI.D.12

Front

How can you determine if a point is a solution to a given inequality?

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

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

Back

The boundary line separates the coordinate plane into two regions: one that satisfies the inequality and one that does not.

Tags

CCSS.HSA.REI.D.12