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 (>, <, ≥, ≤).

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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 reversing the inequality sign if you multiply or divide by a negative number.

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What does the solution of a linear inequality represent?

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The solution of a linear inequality represents a range of values that satisfy the inequality, often expressed as an interval.

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

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A strict inequality uses < or >, meaning the endpoints are not included. A non-strict inequality uses ≤ or ≥, meaning the endpoints are included.

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What is the graphical representation of a linear inequality?

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The graphical representation of a linear inequality is a shaded region on one side of a boundary line, which represents all the solutions to the inequality.

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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 solid line (for ≤ or ≥), then shade the appropriate region.

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What is a word problem in mathematics?

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A word problem is a mathematical question presented in a narrative form, requiring the translation of words into mathematical expressions or equations to find a solution.

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How do you approach solving a word problem?

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To solve a word problem, read carefully, identify the known and unknown variables, translate the words into an equation or inequality, and then solve.

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