Question

I was trying to solve this on my own but was having trouble isolating the x:

x - (x * 0.25) = 3

On algebra.com, it was converted like so:

x - (x * 0.25) = 3
(1 - 0.25) * x = 3     [*** question 1]

And then continues to solve for zero:

(75 / 100) * x = 3
75 * x / 100 = 3
75 * x / 100 - 3 = 0   [*** question 2]
.75 * x - 3 = 0
0 = 0
x = 4

[* question 1] how is this statement derived? This doesn’t seem like distribution.

[* question 2] why solve for zero?

[* question 3] Is there a simpler way to combine like values and solve the equation?

Answer 1

1 Factor x out of the left hand side. x – (x*0.25) => (1-0.25)*x

2 Computers have to do trial and error to get results, it’s looking for whatever will make that equal zero. People can do it a lot more intrinsically.

3

x - (x/4) = 3   -- multiply everything by 4
4x - x = 12     -- suddenly looks a lot easier
3x = 12         -- 4 - 1 = 3      
x = 4           -- 12 / 3 = 4