A number line graph includes the points at real numbers $a$ and $b$, as shown below. Which of the following inequalities expresses an interval that must include the product $ab$ ?

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We can use test values, such as $a=-\dfrac{3}{4}$ and $b=\dfrac{1}{2}$:

$$ab = -\frac{3}{4}\cdot \frac{1}{2}$$ $$= -\frac{3}{8}$$

This fits only the second option.