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

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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.

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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 values of the variable can be less than or equal to a certain number.

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

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The symbol '>' means 'greater than', indicating that the values of the variable must be strictly greater than a certain number.

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How can you convert a linear inequality into slope-intercept form?

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To convert a linear inequality into slope-intercept form (y = mx + b), isolate y on one side of the inequality.

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The slope of the line is -2.

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The graph is a solid line with a slope of -2, and the region above the line is shaded.

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Choose a test point (like (0,0)). If it satisfies the inequality, shade the side containing that point; otherwise, shade the opposite side.

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The solution set is all values of x that are less than 6.

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