Question

communicate your answer

1. how can you use division to solve an inequality?

Explanation:

To solve an inequality using division, if you divide both sides of the inequality by a positive number, the direction of the inequality sign remains the same. For example, if \(2x>4\), dividing both sides by 2 (a positive number) gives \(x > 2\). However, if you divide both sides by a negative number, the direction of the inequality sign must be reversed. For example, if \(-2x>4\), dividing both sides by -2 (a negative number) gives \(x < - 2\). The key is to remember the rule about reversing the inequality sign when dividing by a negative number.

Answer:

To solve an inequality with division: If dividing by a positive number, the inequality sign stays the same. If dividing by a negative number, reverse the inequality sign. For example, for \(2x > 4\), divide by 2 (positive) to get \(x>2\); for \(-2x > 4\), divide by -2 (negative) and reverse sign to get \(x < - 2\).