Solving Linear Inequalities and Word Problems

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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 (>, <, ≥, ≤). It shows the relationship between two expressions.

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What does it mean to solve a linear inequality?

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To solve a linear inequality means to find all values of the variable that make the inequality true.

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What is the difference between an equation and an inequality?

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An equation states that two expressions are equal, while an inequality shows that one expression is greater than or less than another.

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How do you graph a linear inequality on a number line?

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1. Solve the inequality for the variable. 2. Plot the solution on the number line. 3. Use an open circle for < or > and a closed circle for ≤ or ≥. 4. Shade the region that represents the solution.

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What is the solution set of an inequality?

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The solution set of an inequality is the set of all values that satisfy the inequality.

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What does it mean to reverse the inequality sign?

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The inequality sign is reversed when both sides of the inequality are multiplied or divided by a negative number.

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What is a word problem in mathematics?

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A word problem is a mathematical problem that is presented in the form of a narrative or real-life scenario, requiring interpretation and translation into mathematical expressions.

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How do you approach solving a word problem involving inequalities?

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1. Read the problem carefully. 2. Identify the variables. 3. Translate the words into an inequality. 4. Solve the inequality. 5. Interpret the solution in the context of the problem.