1. Problem: We have a number line with colored intervals: yellow (-3 to -2), blue (-2 to -1), pink (-1 to 0), green (0 to 1), purple (1 to 2), and orange (2 to 3). 2. Given: $2A$ lies in the interval $(-2,-1)$, which is the blue interval. 3. To find the interval containing $A$, divide the interval for $2A$ by 2: $$-2 < 2A < -1 \implies \frac{-2}{2} < A < \frac{-1}{2} \implies -1 < A < -\frac{1}{2}$$ 4. The interval $(-1, -\frac{1}{2})$ lies within the blue interval $(-2,-1)$ and pink interval $(-1,0)$. Since $A$ is between $-1$ and $-\frac{1}{2}$, it lies in the pink interval $(-1,0)$. 5. Given $B$ lies in the interval $(1,2)$, which is the purple interval. 6. Therefore: - $A$ lies in the pink interval. - $B$ lies in the purple interval.