Linear Inequalities

Front

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 (>, <, ≥, ≤).

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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.

Front

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.

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.

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.

Front

How do you graph a linear inequality with '>' or '<'?

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You use a dashed line to represent the boundary, indicating that points on the line are not included in the solution.

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How do you graph a linear inequality with '≥' or '≤'?

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You use a solid line to represent the boundary, indicating that points on the line are included in the solution.

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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 satisfy the inequality.

Front

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

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You can test a point not on the line (like (0,0)) to see if it satisfies the inequality. If it does, shade that side; if not, shade the opposite side.

Front

What is the slope-intercept form of a linear equation?

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