Writing Inequalities Using Word Problems

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What is an inequality in mathematics?

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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.

Front

How do you represent a word problem as an inequality?

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To represent a word problem as an inequality, identify the quantities involved, determine the relationship between them, and express that relationship using inequality symbols (>, <, ≥, ≤).

Front

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

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The symbol '≥' means 'greater than or equal to', indicating that the value on the left is either greater than or equal to the value on the right.

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

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The symbol '<' means 'less than', indicating that the value on the left is smaller than the value on the right.

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In the context of word problems, what does 'at least' imply when writing an inequality?

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'At least' implies that the quantity must be greater than or equal to a certain value, which is represented by the '≥' symbol in an inequality.

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In the context of word problems, what does 'more than' imply when writing an inequality?

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'More than' implies that the quantity must be greater than a certain value, which is represented by the '>' symbol in an inequality.

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How do you determine the variable in an inequality from a word problem?

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The variable in an inequality is typically the unknown quantity that you are trying to find, often represented by a letter such as x.

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What is the first step in solving an inequality derived from a word problem?

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The first step is to translate the word problem into a mathematical inequality by identifying the relevant quantities and their relationships.

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How can you check if your solution to an inequality is correct?

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You can check your solution by substituting the value back into the original inequality to see if it holds true.

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What is the significance of the constant term in an inequality?

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The constant term represents a fixed value that affects the outcome of the inequality and helps define the boundary conditions.