Linear Inequalities

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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 ≥.

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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.

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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.

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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'. 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 line (for < or >) or a solid line (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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How do you solve a linear inequality?

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To solve a linear inequality, isolate the variable on one side of the inequality using inverse operations, similar to solving an equation, while remembering to reverse the inequality sign when multiplying or dividing by a negative number.

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What is the difference between a strict and a non-strict inequality?

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A strict inequality (using < or >) does not include the boundary line, while a non-strict inequality (using ≤ or ≥) includes the boundary line.

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

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