Find the union of x- (70/x) < -3

A graph shows the inequality to be true for

... (x < -10) ∪ (0 < x < 7)

or, in interval notation

... (-∞, -10) ∪ (0, 7)

_____

If you add 3 and multiply the inequality by x, you get

... x² +3x -70 < 0

... (x +10)(x -7) < 0

Ordinarily, this would have solution -10 < x < 7, but multiplying by x we have to change the sense of the inequality when x < 0. This makes the solution be as shown above.