# What are the rules when we are dealing with ± sign in any equation?

What are the rules when we are dealing with ± sign in any equation? Like, how does it change when we transpose it to either side.

Eg-

±(a+b)=x ±a=x∓b

Please tell all the other rules including the one mentioned above which we should know while transposing these signs in an equation.

• Welcome to Math.SE! The only thing you need to know is that you should these equations as being two equations written in one: when reading the upper signs, you get the first equation and while reading the lower signs you get the second. For each of these you can use the normal rules of algebra to manipulate the signs. – Hrodelbert Oct 7 '15 at 15:58

The notation is not completely consistent in all cases. But in most cases it's just meant to be read as two different lines/statements where things written on top of each other are part of the respective line from and everything else stays the same in both. This means that

$$\pm (a+b)=x ~\Longleftrightarrow~ \pm a=x\mp b$$

means

\begin{align} +(a+b)=x &~\Longleftrightarrow~ +a=x-b &&\text{ and}\\ -(a+b)=x &~\Longleftrightarrow~ -a=x+b && \end{align} which obviously is true.

Sometimes the logical connector "$\text{and}$" is meant to be an "$\text{or}$" or something else, this depends on the context.

All rules for the $\pm$ and $\mp$ sign can be derived from this and basically are constructed by considering each of the two cases individually.

Some basic manipulations with $\pm$:

\begin{align} \pm a = b &\Longleftrightarrow a = \pm b~\Longleftrightarrow a\mp b =0 \\ \pm a = \pm b &\Longleftrightarrow a=b\\ \pm a = \mp b &\Longleftrightarrow a=-b\\ \pm\pm a &= \mp\mp a = a\\ \pm \mp a &= \mp \pm a=-a\\ \pm (a+b)&=\pm a \pm b\\ &~~\vdots \end{align}

• Although the spirit of your answer is correct, it think it would be helpful if you changed your example: the OP most likely meant to write $\pm(a+b)=x$ implying $\pm a=x\mp b$ (see the space in the OP). – Hrodelbert Oct 8 '15 at 9:29
• @Hrodelbert Of course. Wanted to correct that yesterday but didn't send the edit - thank you! Included now. – Piwi Oct 8 '15 at 18:45