My Math Forum -x=2

 Algebra Pre-Algebra and Basic Algebra Math Forum

 April 25th, 2014, 07:51 AM #1 Senior Member   Joined: Oct 2012 From: Live and work in Saudi but from Italy (British national) Posts: 103 Thanks: 2 Math Focus: Hoping to do something in the future. -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
 April 25th, 2014, 09:07 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,697 Thanks: 2681 Math Focus: Mainly analysis and algebra $-x$ 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 $\frac{1}{2}x=2$?
 April 25th, 2014, 09:10 AM #3 Senior Member     Joined: Apr 2014 From: Greater London, England, UK Posts: 320 Thanks: 156 Math Focus: Abstract algebra $$-x\,=\,2$$ 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 $$x\,=\,-2$$
 April 25th, 2014, 12:38 PM #4 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 -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
 April 25th, 2014, 10:22 PM #5 Senior Member   Joined: Oct 2012 From: Live and work in Saudi but from Italy (British national) Posts: 103 Thanks: 2 Math Focus: Hoping to do something in the future. 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
April 25th, 2014, 10:39 PM   #6
Math Team

Joined: Dec 2013
From: Colombia

Posts: 7,697
Thanks: 2681

Math Focus: Mainly analysis and algebra
Quote:
 Originally Posted by mikeinitaly 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 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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