Question

Which statement about solving inequalities is true?

Adding the same value to both sides of an inequality does not change the solution set.
Subtracting the same value from both sides of an inequality changes the solution set.
When dividing both sides of an inequality by the same positive value, it is necessary to reverse the inequality sign.
When multiplying both sides of an inequality by the same negative value, it is not necessary to reverse the inequality sign.

Answer 1

Only the first statement is true.

- True: Adding (or subtracting) the same number to both sides of an inequality does not change the solution set.
- False: Subtracting the same value does not change the solution set.
- False: Dividing both sides by a positive value preserves the inequality (you do not reverse the sign); only dividing by a negative value reverses it.
- False: Multiplying both sides by a negative value does require reversing the inequality sign.