Solving Linear Inequalities and Word Problems

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What is a linear inequality?

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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. Remember to reverse the inequality sign when multiplying or dividing 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 or a graph on a number line.

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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 uses inequality symbols (>, <, ≥, ≤) and represents a range of solutions.

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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 that satisfy 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 solid line (for ≥ or ≤) or a dashed line (for > or <). Then shade the region that satisfies the inequality.

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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 the problem carefully, identify the relevant information, define variables, set up an equation or inequality, and then solve for the variable.