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April 25th, 2014, 06:51 AM   #1
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-x=2

Hi there,
Sorry but I am starting to learn maths (at 38!) and have come across this equation. The answer is -2, but I dont understand why. Usually I have seen, in this chapter of the book, something like

x+5=5 (to solve for x) so x=0

But this -x=2 has got me confused!
Thanks
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April 25th, 2014, 08:07 AM   #2
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$-x$ means $-1$ times $x$. So you need to think what you need to do to turn that into just $x$.

As a guide, think how you would turn $2x$ or $\frac{1}{2}x$ into $x$. In other words, how would you solve $2x = 2$ and $\frac{1}{2}x=2$?
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April 25th, 2014, 08:10 AM   #3
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$$-x\,=\,2$$
Add $x$ to both sides:
$$x+(-x)\,=\,x+2$$
The LHS is $x-x=0$. So
$$0\,=\,x+2$$
Add $-2$ to both sides:
$$0+(-2)\,=\,x+2+(-2)$$
The LHS is $0-2=-2$, the RHS is $x+2-2=x$. Hence
$$-2\,=\,x$$
which is another way of saying
$$x\,=\,-2$$
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April 25th, 2014, 11:38 AM   #4
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-a = b is really -a = +b

Always ok to change ALL signs (not a few... but ALL!)
So:
+a = -b

-a + b - c = d - e - f
same as:
a - b + c = -d + e + f
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April 25th, 2014, 09:22 PM   #5
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Thanks for the reply. Sorry but what is LHS and RHS?

Also, Denis, if an equation must be balanced, how does -a=+b
Surely the value of the terms on each side of the equation are different?
M
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April 25th, 2014, 09:39 PM   #6
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Quote:
Originally Posted by mikeinitaly View Post
Thanks for the reply. Sorry but what is LHS and RHS?
LHS = Left hand side of the equation (everything before the '=').
RHS = Right hand side of the equation (everything after the '=').

Quote:
Originally Posted by mikeinitaly View Post
Also, Denis, if an equation must be balanced, how does -a=+b
Surely the value of the terms on each side of the equation are different?
M
a and b represent numbers.

So if a = 2 and b = -2, the equation is satisfied. But the important part of Denis' post is that if the first equation (-a = +b) is satisfied, so is the second (+a = -b).
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