A liquid is cooled by 10°C and then heated by 4°C. If its final temperature is 17°C, what was its initial temperature?

Let $T_i$ be the initial temperature of the liquid.
The liquid was first cooled by $10^\circ\text{C}$, so its temperature became $T_i - 10$.
Then, its temperature was increased by $4^\circ\text{C}$, so it became $(T_i - 10) + 4$.
The final temperature is given as $17^\circ\text{C}$.

Add 6 to both sides of the equation:

The initial temperature of the liquid was $23^\circ\text{C}$.