Dec 4 HW - 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 ≥). It represents a range of possible solutions rather than a single solution.

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

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'>' 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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'<'' 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 is the solution set of a linear inequality?

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The solution set of a linear inequality is the set of all values that make the inequality true, often represented as a shaded region on a graph.

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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 if you multiply or divide by a negative number.

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What is the difference between a linear equation and a linear inequality?

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A linear equation has an equal sign and represents a single solution, while a linear inequality has an inequality sign and represents a range of solutions.

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

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'≥' means 'greater than or equal to'. It indicates that the value on the left side is either greater 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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'≤' means 'less than or equal to'. It indicates that the value on the left side is either less than or equal to the value on the right side.

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How can you check if a value is a solution to a linear inequality?

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To check if a value is a solution, substitute it into the inequality. If the resulting statement is true, then the value is a solution.