Situations Represented by Equations and Inequalities

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What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

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What does the symbol '>' represent in an inequality?

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The symbol '>' means 'greater than'. For example, in the inequality 5 > 3, it indicates that 5 is greater than 3.

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What does the symbol '<' represent in an inequality?

Back

The symbol '<' means 'less than'. For example, in the inequality 2 < 4, it indicates that 2 is less than 4.

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What does the symbol '≥' represent in an inequality?

Back

The symbol '≥' means 'greater than or equal to'. For example, in the inequality x ≥ 10, it indicates that x can be 10 or any number greater than 10.

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What does the symbol '≤' represent in an inequality?

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The symbol '≤' means 'less than or equal to'. For example, in the inequality y ≤ 5, it indicates that y can be 5 or any number less than 5.

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How do you solve a simple inequality?

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To solve a simple inequality, isolate the variable on one side of the inequality sign by performing the same operations on both sides, similar to solving an equation.

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What is a linear equation?

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A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

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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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What is a solution to an inequality?

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A solution to an inequality is any value that makes the inequality true. For example, in the inequality x > 3, any number greater than 3 is a solution.

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What does it mean to graph an inequality?

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Graphing an inequality involves shading a region of the graph that represents all the solutions to the inequality, using a dashed line for '<' or '>' and a solid line for '≤' or '≥'.