This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Step 1: Set up the equation based on the given information. Let be the initial temperature of the liquid. The liquid was first cooled by , so its temperature became . Then, its temperature was increased by , so it became . The final temperature is given as .
Step 2: Formulate the equation and solve for . Add 6 to both sides of the equation:
The initial temperature of the liquid was .
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Set up the equation based on the given information. Let T_i be the initial temperature of the liquid.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.