Linear Inequalities & Graphs

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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 (such as <, >, ≤, or ≥). It represents a region of the coordinate plane.

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What does the symbol '>' mean in a linear inequality?

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The symbol '>' means 'greater than'. It indicates that the value on the left side of the inequality is larger than the value on the right side.

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What does the symbol '<' mean in a linear inequality?

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The symbol '<' means 'less than'. It indicates that the value on the left side of the inequality is smaller than the value on the right side.

Front

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

Front

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

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

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What is the solution set of a linear inequality?

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The solution set of a linear inequality is the set of all points (x, y) that make the inequality true, represented graphically as a shaded region on the coordinate plane.

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

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

Front

How do you determine which side of the line to shade when graphing a linear inequality?

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To determine which side to shade, pick a test point not on the line (commonly (0,0)). Substitute it into the inequality. If the inequality holds true, shade the side containing the test point.

Front

What is the inequality represented by the graph of a horizontal line at y = -2?

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