A graph shows the inequality to be true for
... (x < -10) ∪ (0 < x < 7)
or, in interval notation
... (-∞, -10) ∪ (0, 7)
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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.
