Answer:
Let's start by writing the given statement as an equation.
Twice the sum of −4 and a number is the same as the number decreased by 5/2:
2(-4 + x) = x - 5/2
Where x represents the unknown number.
Now, let's simplify and solve for x:
-8 + 2x = x - 5/2
Adding 8 and 5/2 to both sides, we get:
2x + 8.5/2 = x + 1.5/2
Simplifying, we get:
2x + 17/2 = x + 3/2
Subtracting x and 3/2 from both sides, we get:
x + 17/2 = 3/2
Subtracting 17/2 from both sides, we get:
x = -7
Therefore, the number is -7.
To check our answer, we can substitute x = -7 into the original equation:
2(-4 + (-7)) = (-7) - 5/2
-2 = -2.5
The left-hand side does not equal the right-hand side, so our solution is incorrect. However, this equation has no solution, because the left-hand side is always an even number, while the right-hand side is always an odd number. Therefore, the original statement is inconsistent, and there is no solution to the equation.