Mathematics ACT Aspire Practice Test

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Study for the Mathematics ACT Aspire Test. Use flashcards, multiple choice questions, and detailed explanations. Get prepared for your exam!

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What is the first step in solving a two-step inequality?

Multiply both sides by a negative number
Divide both sides by a positive number
Add or subtract
Switch the sides of the inequality

The correct answer is: Add or subtract

To solve a two-step inequality, the first step typically involves isolating the variable, which often starts with adding or subtracting a constant from both sides. This is because many inequalities have a term that needs to be moved away from the variable in order to simplify the expression and work towards isolating it. For instance, if the inequality is of the form $2x + 3 < 7$, the first step would be to subtract 3 from both sides, leading to $2x < 4$. Once the constant is removed, the next step would be to deal with the coefficient of the variable, which will typically involve multiplying or dividing. Other options, like multiplying by a negative number or switching the sides of the inequality, are actions that apply later in the problem-solving process or in specific contexts. It's essential to begin with addition or subtraction because those operations help clarify the relationship between the variable and the constant involved. This foundational step provides clarity and sets the stage for the following operations that will eventually lead to a solution.