Question

According to the properties of inequality, when should the inequality symbol be reversed when solving a two-step inequality in the form below?

a x + b greater-than c
when a is positive
when a is negative
when b is positive
when b is negative

Answer 1

When you multiply or divide both sides by a negative number.

So for ax + b > c, you reverse the inequality only if a is negative (because you divide by a to isolate x). Subtracting b does not reverse the sign.

Example: -2x + 3 > 7 → -2x > 4 → x < -2 (inequality reversed).