Final answer:
The algebraic expression description is 6(x + 2) = 42, where x is the number thought of initially. To find the value of x, divide both sides by 6 and then subtract 2, which reveals x equals 5.
Step-by-step explanation:
The algebraic expression based on the sequence of operations provided is: Let the number you think of be represented as x. First, you add 2 to this number, giving you x + 2. Next, you multiply the sum by 6, resulting in 6(x + 2). If this result equals 42, then the full algebraic expression can be written as 6(x + 2) = 42.
Using principles of mathematics, like the ones mentioned in the examples, to isolate the variable x, you'd perform the following steps:
- Divide both sides of the equation by 6 to reverse the multiplication, which leaves you with x + 2 = 7.
- Next subtract 2 from both sides to solve for x, which gives you x = 5.
This process of using algebra to solve for an unknown number can often present different methods that lead to the same solution, which is a valuable lesson in flexibility and verification within mathematics.