Reciprocal inequality: Solve the inequality.

Since we need to multiply both sides of the inequality by x, and since we have separate rules for positive and negative multiplication, we need to consider these two cases separately. Furthermore, because of the x factor in the denominator, we know that x can not be zero.

When x is positive, we can use the positive multiplication rule to multiply by x to get , or .

When x ix negative, we can use the negative multiplication rule and change the direction of the inequality to get , or