4. На координатной прямой отмечены числа 0, а и b. Отметьте на этой прямой какое-нибудь число х так, чтобы при этом выполнялись три ax <0. условия: х - а <0,x-b<0, b

4. Рассмотрим условия: $$x - a < 0$$, $$x - b < 0$$, $$\frac{ax}{b} < 0$$.

Из первых двух неравенств следует: $$x < a$$ и $$x < b$$. Так как $$a$$ и $$b$$ положительные, а $$b > a$$, то $$x < a$$.

Из третьего неравенства $$\frac{ax}{b} < 0$$. Так как $$a > 0$$ и $$b > 0$$, то это неравенство выполняется, когда $$x < 0$$.

Таким образом, число $$x$$ должно быть меньше нуля.

Отметим на координатной прямой числа 0, a, b и x.

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