kaze950 said:
(1/10)(x+8) - (1/15)(x-5)
which becomes
(x+8/10) - (x-5/15)
You're not getting it. This step you have written is incorrect.
x+8/10 = x+(8/10) = x+(4/5) = (5x+4)/5
x-5/15 = x-(5/15) = x-(1/3) = (3x-1)/3
I suspect that is NOT what you intended.
Written carefully, one gets
(1/10)(x+8) - (1/15)(x-5) = 1
Multiply by 5, just for practice
(1/2)(x+8) - (1/3)(x-5) = 5
Multiply by 3
(3/2)(x+8) - (x-5) = 15
Multiply by 2
(3)(x+8) - (2)(x-5) = 30 (Of course, would could have multiplied by 30 in the first place.)
Expand, using the Distributive Property
3x + 24 - 2x + 10 = 30
Rearrange (Commutative Property)
3x - 2x + 24 + 10 = 30
Combine Like Term (Associative Property)
(3x - 2x) + (24 + 10) = 30
x + 34 = 30
Subtract 34
x = 30 - 34 = -4
There are NO holes in that notation. Every step says what it is supposed to mean. Careful, clear, consistent, comprehensible. No slopiness. You will pay a price for that, later.