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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 $-1.87$?

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  • $\begingroup$ Why didn’t you add $1.87x$ instead of subtracting $1.496$? That would get you immediately $1.496=2.87x$. $\endgroup$ – Michael Hoppe Apr 2 '18 at 10:15
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$$-1.87-1=-2.87$$

If it helps

$$-1.87-1=-(1.87+1)=-2.87$$

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  • $\begingroup$ I understand that -(1.87+1)= -2.87, but the issue is that I cannot locate where the 1 was pulled from in the equation. $\endgroup$ – Aden. G Apr 2 '18 at 7:25
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    $\begingroup$ $-1.87x -x =-1.87x-1x$ , just like $1x=x$, we don't write them explicitly most of the time. $\endgroup$ – Siong Thye Goh Apr 2 '18 at 7:27
  • $\begingroup$ I think I understand now, thank you $\endgroup$ – Aden. G Apr 2 '18 at 7:58
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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 $$-1.87x - 1x$$$$ = (-1.87-1)x$$$$= -2.87x$$

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