Final answer:
The algebraic expression translating the statement is 2x + 6 = x - 3. By introducing the variable x for the unknown number, we express twice the number and the sum with six, and equate it to the number subtracted by three.
Step-by-step explanation:
To translate the statement "the sum of twice a number and six is the same as three subtracted from the number itself" into an algebraic expression, we begin by assigning a variable to the unknown number. We can let x represent this unknown number. According to the statement, twice this number can be written as 2x, and the sum of twice the number and six is 2x + 6.
The second part of the statement involves subtracting three from the number itself, which is expressed as x - 3. The phrase "is the same as" indicates equality, so we can equate the two expressions to form an equation: 2x + 6 = x - 3.
To solve for x, we usually would first simplify the equation by subtracting x from both sides, yielding x + 6 = -3, and then further subtract six from both sides to get x = -9.