Mathematics ACT Aspire Practice Test

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Study for the Mathematics ACT Aspire Test. Master concepts through a mix of questions. Dive into explanations and hints for a thorough understanding. Elevate your test readiness!

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What happens to the inequality symbol when you multiply both sides of an inequality by a negative number?

The symbol remains the same
The symbol must be reversed
The symbol changes only if one side is positive
The symbol no longer applies

The correct answer is: The symbol must be reversed

When you multiply both sides of an inequality by a negative number, the direction of the inequality symbol must be reversed. This is a key rule in working with inequalities that stems from the properties of real numbers. To understand why this is the case, consider a simple inequality such as -2 < 3. If we multiply both sides by -1, we get 2 and -3. The relationship between these two values has changed: 2 is actually greater than -3, so the correct inequality after multiplying by -1 is 2 > -3, demonstrating that the symbol has indeed reversed. This rule ensures that the inequality remains true under the new condition created by multiplying by a negative number. Not applying this reversal would lead to incorrect conclusions about the relationship between the two values. The other options don't correctly describe what happens to the inequality symbol when multiplied by a negative number; the symbol does not remain the same, does not change based solely on positivity or negativity of one side, and it always applies.