# $1.87= x/(0.80-x)$ Easy question with one difficult step

I am doing some very basic algebra work, and one of the examples has the question and how to solve for $x$. The answer looks like $$1.87=\frac{x}{0.80-x}$$ multiply both sides by $0.80-x$ simplified $$1.87(0.80-x)=x$$ which expanded looks like $$1.496-1.87x=x$$ subtract $1.496$ from both sides

$$-1.87x=x-1.496$$ subtract $x$ from both sides $$-1.87x-x=x-1.496-x$$ simplified $$-2.87x=-1.496$$ solved $$\frac{-2.87x}{-2.87} =\frac{-1.496}{-2.87}$$ $$x=0.52125$$

I can follow all of this and understand the steps, but where I am getting lost is when $-1.87x$ becomes $-2.87x$. Why does this happen? Would subtracting an $x$ just create $-1.87$?

• Why didn’t you add $1.87x$ instead of subtracting $1.496$? That would get you immediately $1.496=2.87x$. – Michael Hoppe Apr 2 '18 at 10:15

$$-1.87-1=-2.87$$
$$-1.87-1=-(1.87+1)=-2.87$$
• $-1.87x -x =-1.87x-1x$ , just like $1x=x$, we don't write them explicitly most of the time. – Siong Thye Goh Apr 2 '18 at 7:27
In the expression $$-1.87x-x$$, if there is no coefficient of the second term $$x$$, the coefficient of that term is understood to be $$1$$. Thus, $$-1.87x - x$$ can be rewritten as $$-1.87x - 1x$$$$= (-1.87-1)x$$$$= -2.87x$$