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 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.

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CCSS.HSA.REI.D.12

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How do you graph a linear inequality?

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1. Graph the corresponding linear equation as a solid line (for ≥ or ≤) or a dashed line (for > or <). 2. 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.

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CCSS.8.EE.C.8B

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

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Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

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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 does the solution set of a system of linear inequalities look like?

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

Tags

CCSS.HSA.REI.D.12

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How can you express a system of inequalities algebraically?

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A system of inequalities can be expressed using multiple inequalities, such as: y > 2x - 4 and y < 2.

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

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The boundary line divides the coordinate plane into two regions, one where the inequality holds true and one where it does not.

Tags

CCSS.HSA.REI.D.12

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What does it mean for a point to be a solution to a linear inequality?

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A point is a solution to a linear inequality if it makes the inequality true when substituted into it.