Solve Multi-Step Inequalities word problems

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What is a multi-step inequality?

Back

A multi-step inequality is an inequality that requires more than one step to solve, often involving operations such as addition, subtraction, multiplication, or division.

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How do you represent a word problem as an inequality?

Back

Identify the key quantities and relationships in the problem, then translate them into an inequality using symbols like <, >, ≤, or ≥.

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What does it mean when a problem states 'no more than'?

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'No more than' indicates a maximum limit, which translates to a less than or equal to (≤) inequality.

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What does it mean when a problem states 'at least'?

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'At least' indicates a minimum requirement, which translates to a greater than or equal to (≥) inequality.

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How do you solve a multi-step inequality?

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To solve a multi-step inequality, isolate the variable on one side using inverse operations, while maintaining the direction of the inequality.

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What is the solution set of an inequality?

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The solution set of an inequality is the range of values that satisfy the inequality, often represented on a number line.

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How do you check the solution of an inequality?

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Substitute a value from the solution set back into the original inequality to verify that it holds true.

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What is the significance of the boundary point in an inequality?

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The boundary point is the value that makes the inequality true; it is included in the solution set if the inequality is ≤ or ≥.

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What is the difference between strict and non-strict inequalities?

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Strict inequalities (<, >) do not include the boundary point, while non-strict inequalities (≤, ≥) do include it.

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How do you graph an inequality on a number line?

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Use an open circle for strict inequalities and a closed circle for non-strict inequalities, then shade the appropriate region.