# Rearranging Equations

## Keeping things balanced

Sometimes we might write $$=$$ without really thinking about its meaning. Simply put; $\text{left hand side} = \text{right hand side}$ This means that the left hand side (LHS) has exactly the same value as the right hand side (RHS). So, the big importance of this is that if we do the same operation to both sides, they'll still be the same! We can see with numbers: \begin{align} 5 &= 5 \\5 + 3 &= 5 + 3 \\8 &= 8 \end{align}

## Playing with letters, finding $$x$$

The same thing can be used when 'scary' letters are involved. \begin{align} 5 + x &= 3 + 2x \\5 + x - x &= 3 + 2x - x \\5 &= 3 + x \\5 - 3 &= 3 + x - 3 \\2 &= x \end{align} There, we've just solved our first equation! By adding or substracting the same amount from each side, the LHS and RHS are equal at every step. Let's try one with multiplication: \begin{align} 4x - 2 &= 10 \\ 4x - 2 + 2 &= 10 + 2 \\ 4x &= 12 \\ \tfrac{4x}{4} &= \tfrac{12}{4} \\ x &= 3 \end{align}

Now you've got all the tools you need to start solving linear equations.