#### Answer

The solution to this equation is all real numbers.
Using set notation: {x|x is an element of the Real Numbers}

#### Work Step by Step

4x + 1 - 5x = 5 - (x + 4)
Solving the equation, we start by using the distributive property to distribute a -1 across the parentheses.
4x + 1 - 5x = 5 -x - 4
Next, we can regroup each side of the equation so that like terms are together.
4x - 5x + 1 = 5 - 4 - x
Then, combine like terms:
-x + 1 = 1 - x
Add x to both sides:
-x + x + 1 = 1 - x + x
1 = 1
Since our variable term completely cancelled out, and our numbers in our last line show an equality, the solution is: ALL REAL NUMBERS