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 range of possible values for a variable.

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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 inequality and an equation?

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An inequality shows a range of values that satisfy a condition, while an equation shows that two expressions are equal.

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

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1. Graph the boundary line (dashed for < or >, solid for ≤ or ≥). 2. Shade the region that satisfies the inequality.

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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 is the first step in solving a linear inequality?

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The first step is to simplify both sides of the inequality, if necessary.

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What does it mean to isolate the variable in an inequality?

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To isolate the variable means to manipulate the inequality so that the variable is on one side and all other terms are on the other side.

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What happens to the inequality sign when you multiply or divide by a negative number?

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When you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign.