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- Feb 5, 2012

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**SplashDamage's question from Math Help Forum,**

Hi SplashDamage,if I have 4 + ((a - 1) / 12) = 24

Why can I not move the 12 over to the other side first? Making it 4 + a - 1 = 24 * 12

Howecome I have to move the 4 over first? I never really knew why, possibly there is an order to moving things over the = sign?

Thanks for any help.

There is no such thing as "moving" a term to the other side. A equal sign means that both quantities same quantitative amount. Therefore you can add, subtract, divide or multiply both sides of the equality by the same number and equality will still hold.

So you cannot "move" 12 over to the other sides, but you can multiply the two sides by 12. Similarly you cannot move 4 over to the other side, but you can subtract 4 from both sides.

Suppose if you want to find \(a\) in the equation, \(4 + \dfrac{a - 1}{12} = 24\).

First we can multiply both sides of the equation by 12,

\[12\left(4+\frac{a - 1}{12}\right)=12\times 24\]

\[\Rightarrow (12\times 4)+\left(12\times \frac{a-1}{12}\right)=288\]

\[\Rightarrow 48+a-1=288\]

\[\Rightarrow 47+a=288\]

Now we shall subtract 47 from both sides,

\[47+a-47=288-47\]

\[a=241\]

Another method is to subtract 4 first, starting from the original equation.

\[4 + \frac{a - 1}{12} = 24\]

\[\Rightarrow 4 + \frac{a - 1}{12}-4=24-4\]

\[\Rightarrow \frac{a - 1}{12}=20\]

Now we shall multiply both sides by 12,

\[\Rightarrow 12\times \dfrac{a - 1}{12}=20\times 12\]

\[\Rightarrow a - 1=240\]

Finally add 1 to both sides,

\[a=241\]