Question

How do you solve `27- 11x = x - 33`?

Answer 1

`x=5`

Explanation:

`27-11x=x-33`

You want the answer to be of the form `x=?`

So, start by "undoing" the part of the equation furthest away from the variable: in this case, `+27` and `-33` are furthest away from the `x` on both sides

1. For this explanation, we will "undo" the `-33` on both sides

`27-11x+33=x-33+33`

2. Then collect like terms

`27+33-11x=x`

`60-11x=x`

It should be noted that it is possible to start by "undoing" the `+27` in a similar way

Now we want to have all the `x`'s on one side so that it can be of the form `x=?`

3. "Undo" the `-11x` on both sides

`60-11x+11x=x+11x`

4. Collect like terms

`60=12x`

To "solve" the equation the answer must be a "singular" `x=?`

5. "Undo" the `12*x` on both sides

`60/12=(12x)/12`

6. Collect like terms and cancel appropriately

`5=x`

Therefore

`x=5`

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*Footnote*

In this context, "undo" means to "do the opposite of", so to "undo" a `-2` it is necessary to `+2`. However, this must be done on both sides of the equation in order to maintain its balance.

Eg: if 1kg was to be added to one side of a balance scale, the same weight must be added to the other side so that the balance is maintained.