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Movement As Arithmetic

If you solve this equation,

$$\frac{2x-7}{3}=5$$

you might multiply each side by three,

$$3\times\left(\frac{2x-7}{3}\right)=\left(5\right)\times3$$

$$2x-7=15$$

then add seven to each side,

$$\left(2x-7\right)+7=\left(15\right)+7$$

$$2x=22$$

and finish by dividing each side by two:

$$\frac{\left(2x\right)}{2}=\frac{\left(22\right)}{2}$$

$$x=11$$

These three arithmetic operations can be modelled in a particular, visual manner. When done correctly, they have the same mathematical effect as the ``normal'' way. Let's examine each operation in detail.