FTCE General Knowledge Math Practice Test

In the inequality -3x ≥ 1, what happens when you divide by a negative number?

1. The inequality stays the same

2. The inequality sign reverses

3. The solution becomes negative

4. No change occurs in the inequality

The correct answer is: The inequality sign reverses

When dividing or multiplying both sides of an inequality by a negative number, the direction of the inequality sign must be reversed. This is a fundamental rule in algebra that ensures the relationship remains true even after performing the operation. In the given inequality, -3x ≥ 1, if we divide both sides by -3, the sign changes from '≥' to '≤'. This results in the inequality -3x ≥ 1 becoming x ≤ -1. Thus, your selection reflects this crucial principle of inequalities, confirming that the inequality sign indeed reverses when dividing by a negative number.