Introduction:
To find a number that, when multiplied by 2, is increased by 80, we can set up an algebraic equation. This equation will help us find the unknown number, and solve for it using basic algebraic operations.

Problem:
Let's assume the unknown number is represented by the variable "x". The problem states that when this number is multiplied by 2, it is increased by 80. Mathematically, this can be written as:

2x = x + 80

Solving the equation:
To solve this equation, we need to isolate the variable "x" on one side of the equation. We can do this by performing algebraic operations.

Subtracting "x" from both sides:
2x - x = x + 80 - x

Simplifying the left side:
x = 80

Interpreting the solution:
The solution to the equation is x = 80. This means that the unknown number we were looking for is 80.

Verification:
To verify our solution, we can substitute the value of x back into the original equation and check if it satisfies the condition.

2(80) = 80 + 80
160 = 160

The equation is satisfied, indicating that the number 80, when multiplied by 2, is indeed increased by 80.

Conclusion:
The number that, when multiplied by 2, is increased by 80 is 80.