Final answer:
The student's algebraic identity involves finding an unknown number that, when summed with six and doubled, results in being five less than itself. The equation derived from the problem statement is 2(x + 6) = x - 5, which simplifies to x = -17 as the solution.
Step-by-step explanation:
The student is asking to verify an algebraic identity involving addition, multiplication, and subtraction. We are given that 'If the sum of a number and six is doubled, the result is five less than the number'. To find and verify the identity, first, let's define the unknown number as x. The statement can be turned into an equation: 2(x + 6) = x - 5. Simplifying this, we get 2x + 12 = x - 5. Subtracting x from both sides yields x + 12 = -5. Finally, subtracting 12 from both sides gives x = -17, which is the solution to the problem presented.
While solving this problem, we use several operations and rules regarding signs:
- When two positive numbers add, the answer has a +ve sign, e.g., 3+2 = 5.
- In subtraction, we change the sign of the subtracted number and then follow the rules of addition.
- When a positive and a negative number are multiplied, the answer has a -ve sign.
- This type of problem helps to understand how to manipulate and solve algebraic equations, reinforcing the rules of adding, multiplying, and subtracting numbers with different signs.