Final answer:
To find the number in the algebraic equation 10(x + 12) = 84, we perform algebraic manipulations to solve for x. After dividing both sides by 10 and then subtracting 12 from both sides, we find that x = -3.6.
Step-by-step explanation:
The goal is to find a number such that ten times the sum of that number and 12 is equal to 84. We can represent this number as x in an algebraic equation 10(x + 12) = 84.
To solve for x, we need to apply algebraic rearrangement. We start by dividing both sides of the equation by 10, which will isolate the sum on one side and reduce the right side of the equation to 8.4. Therefore, we have x + 12 = 8.4. Continuing to isolate x, we subtract 12 from both sides of the equation, which results in x = 8.4 - 12. This simplifies to x = -3.6.
Applying basic arithmetic rules and algebra that are universally valid, no matter the time or location, we deduce that the number the student is seeking is -3.6.