Solving Two Step Inequalities

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What is a two-step inequality?

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A two-step inequality is an inequality that requires two operations to isolate the variable. It typically involves addition or subtraction followed by multiplication or division.

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How do you represent a situation where a person can spend no more than a certain amount?

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You can represent this situation with an inequality where the total cost is less than or equal to the maximum amount. For example, if the maximum is $40, the inequality would be: total cost ≤ 40.

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It represents the maximum number of rides (x) Daniel can take at the fair, given that admission costs $10 and each ride costs $1.50.

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What is the significance of using an open circle when graphing inequalities?

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

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

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It represents the time (x) it will take for the temperature in the ice rink to fall below 50°F, starting from 71°F and decreasing by 3.5°F each hour.

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You would draw a number line, place an open circle at 4, and shade to the left to indicate all numbers less than 4.

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What is the difference between a filled-in dot and an open circle in graphing inequalities?

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A filled-in dot indicates that the number is included in the solution (≤ or ≥), while an open circle indicates it is not included (< or >).