Solving MultiStep Inequalities

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What is a multi-step inequality?

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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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What does it mean to 'undo' an operation in solving inequalities?

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To 'undo' an operation means to perform the inverse operation to isolate the variable. For example, if you added a number, you would subtract it to undo that operation.

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The first step is to subtract 20 from both sides of the inequality.

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What happens to the inequality sign when you multiply or divide by a negative number?

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When you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign.

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How do you represent a situation where you cannot exceed a certain amount using an inequality?

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You can represent it using a 'less than or equal to' (≤) inequality.

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What is the inequality that represents spending at most $1200 on a laptop with a $400 down payment?

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What does the solution x ≥ 2 mean in terms of a number line?

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It means that the solution includes all numbers greater than or equal to 2, represented by a closed dot at 2 and a line extending to the right.

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What is the correct inequality for a taxi fare of $2.50 per mile plus a $5 fee that cannot exceed $20?

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How do you graph the inequality x > 3 on a number line?

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You place an open dot at 3 and draw a line extending to the right.