Solving Inequalities (Word Problems)

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What is an inequality?

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An inequality is a mathematical statement that compares two expressions using inequality symbols (>, <, ≥, ≤) to show that one expression is greater than, less than, or equal to another.

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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 sign 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 does it mean to 'factor' an expression?

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Factoring an expression means rewriting it as a product of its factors, which are simpler expressions that, when multiplied together, give the original expression.

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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, often represented on a number line.

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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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To graph a linear inequality on a number line, use an open circle for < or > and a closed circle for ≤ or ≥, then shade the region that represents the solution set.

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What is the distributive property?

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The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by each term inside a parenthesis.

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How do you combine like terms?

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To combine like terms, add or subtract the coefficients of terms that have the same variable raised to the same power.

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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 translate a word problem into an inequality?

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To translate a word problem into an inequality, identify keywords (like 'more than', 'less than', 'at least', 'no more than') and express the relationships using inequality symbols.